13. Q13ab
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Similar Question 1
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Graph <code class='latex inline'>f^{-1}(x)</code> for <code class='latex inline'>y \geq 0.75</code>.</p>
Similar Question 2
<p>Is the inverse of a quadratic function also a function? Give a reason for your answer. </p>
Similar Question 3
<p>Given the graph of <code class='latex inline'>f(x)</code>, graph the inverse relation.</p><img src="/qimages/885" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>The height of a ball thrown from a balcony can be modelled by the function <code class='latex inline'>h(t) = -5t^2 + 10t + 35</code>, where <code class='latex inline'>h(t)</code> is the height above the ground, in metres, at time <code class='latex inline'>t</code> seconds after its is thrown. </p><p>Write <code class='latex inline'>h(t)</code> in vertex form.</p>
<p><strong>(a)</strong> Sketch the graph of <code class='latex inline'>f(x) = 3(x - 2)^2 - 2</code>.</p><p><strong>(b)</strong> Sketch the graph of its inverse on the same axes.</p>
<p>A function <code class='latex inline'>g</code> is defined by <code class='latex inline'>g(x) = 4(x - 3)^2 + 1</code></p><p>What is the equation for the inverse of <code class='latex inline'>g(x)</code>? Show your work.</p>
<p><strong>(a)</strong> Graph <code class='latex inline'>g(x) = - \sqrt{x}</code> for <code class='latex inline'>x \geq 0</code>.</p><p><strong>(b)</strong> Graph its inverse on the same axes.</p><p><strong>(c)</strong> State the domain and range of <code class='latex inline'>g^{-1}(x)</code>.</p><p><strong>(d)</strong> Determine the equation for <code class='latex inline'>g^{-1}(x)</code>. </p>
<p>Given <code class='latex inline'>f(x) = 7 - 2(x - 1)^2</code>, <code class='latex inline'>x \geq 1</code>, determine <code class='latex inline'> \displaystyle f^{-1}(2a + 7) </code></p>
<p>For <code class='latex inline'>-2 < x < 3</code> and <code class='latex inline'>f(x) = 3x^2 - 6x</code>, determine</p><p><strong>(a)</strong> the domain and range of <code class='latex inline'>f(x)</code></p><p><strong>(b)</strong> the equation of <code class='latex inline'>f^{-1}(x)</code> if <code class='latex inline'>f(x)</code> is further restricted to <code class='latex inline'>1 < x < 3</code>.</p>
<p>Given <code class='latex inline'>h(x) = x^2 - 2x</code>, determine the following</p><p>a) <code class='latex inline'>h(x - 3)</code></p><p>b) Find the inverse function of <code class='latex inline'>h(x)</code> by restricting the domain. State the domain.</p>
<p>You are given the relation <code class='latex inline'>x = 4 - 4y + y^2</code>.</p><p>(a) Graph the relation.</p><p>(b) Determine the domain and range of the relation.</p><p>(c) Determine the equation of the inverse.</p><p>(d) Is the inverse a function? Explain.</p>
<p>The height of a ball thrown from a balcony can be modelled by the function <code class='latex inline'>h(t) = -5t^2 + 10t + 35</code>, where <code class='latex inline'>h(t)</code> is the height above the ground, in metres, at time <code class='latex inline'>t</code> seconds after its is thrown. </p><p>Determine the domain and range of <code class='latex inline'>h(t)</code>.</p>
<p>State the domain and range of the inverse relation.</p><img src="/qimages/892" />
<p>For each function <code class='latex inline'>f</code>, find <code class='latex inline'>f^{-1}</code>.</p><p><code class='latex inline'>f(x) = x^2 + 4</code></p>
<p>Is the inverse of a quadratic function also a function? Give a reason for your answer. </p>
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Determine the vertex of the parabola.</p>
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Graph <code class='latex inline'>f(x)</code> by converting it to vertex form.</p>
<p>The height of a ball thrown from a balcony can be modelled by the function <code class='latex inline'>h(t) = -5t^2 + 10t + 35</code>, where <code class='latex inline'>h(t)</code> is the height above the ground, in metres, at time <code class='latex inline'>t</code> seconds after its is thrown. </p><p>Determine the model that describes time in terms of the height.</p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, sketch the graph of the inverse relation.</p><img src="/qimages/892" />
<p>Given <code class='latex inline'>f(x) = 7 - 2(x - 1)^2</code>, <code class='latex inline'>x \geq 1</code>, determine <code class='latex inline'>f(3)</code></p>
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Determine the domain and range of <code class='latex inline'>f^{-1}(x)</code> for <code class='latex inline'>y \geq 0.75</code>.</p>
<p>Given the graph of <code class='latex inline'>f(x)</code>, graph the inverse relation.</p><img src="/qimages/885" />
<p>Given <code class='latex inline'>f(x) = \frac{1}{2}(x - 5)^2 + 3</code>, find the equation for <code class='latex inline'>f^{-1}(x)</code> for the part of the function where <code class='latex inline'>x \leq 5</code>. Use a graphing calculator to graph <code class='latex inline'>f^{-1}(x)</code>. </p>
<p>Each graph shows a function <code class='latex inline'>f</code> that is a parabola or a branch of a parabola.</p><img src="/qimages/886" /> <ul> <li>i) Determine <code class='latex inline'>f(x)</code></li> <li>ii) Graph <code class='latex inline'>f^{-1}</code></li> <li>iii) State restrictions on the domain or range of <code class='latex inline'>f</code> to make its inverse a function.</li> <li>iv) Determine the equation(s) for <code class='latex inline'>f^{-1}</code>.</li> </ul>
<p>Is the inverse relation a function? Why or why not?</p><img src="/qimages/892" />
<p>Each graph shows a function <code class='latex inline'>f</code> that is a parabola or a branch of a parabola.</p><img src="/qimages/887" /> <ul> <li>i) Determine <code class='latex inline'>f(x)</code></li> <li>ii) Graph <code class='latex inline'>f^{-1}</code></li> <li>iii) State restrictions on the domain or range of <code class='latex inline'>f</code> to make its inverse a function.</li> <li>iv) Determine the equation(s) for <code class='latex inline'>f^{-1}</code>.</li> </ul>
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Graph <code class='latex inline'>f^{-1}(x)</code> for <code class='latex inline'>y \geq 0.75</code>.</p>
<p>Each graph shows a function <code class='latex inline'>f</code> that is a parabola or a branch of a parabola.</p><img src="/qimages/889" /> <ul> <li>i) Determine <code class='latex inline'>f(x)</code></li> <li>ii) Graph <code class='latex inline'>f^{-1}</code></li> <li>iii) State restrictions on the domain or range of <code class='latex inline'>f</code> to make its inverse a function.</li> <li>iv) Determine the equation(s) for <code class='latex inline'>f^{-1}</code>.</li> </ul>
<p>Given <code class='latex inline'>f(x) = 2x^2 - 1</code>, determine the equation of the inverse. </p>
<p>The formula <code class='latex inline'>A = \pi r^2</code> is convenient for calculating the area of a circle when the radius is known. What is the inverse of the relation, and what can it be used for? Explain.</p>
<p>Given <code class='latex inline'>f(x) = 7 - 2(x - 1)^2</code>, <code class='latex inline'>x \geq 1</code>, determine <code class='latex inline'> \displaystyle f^{-1}(x) </code></p>
<p>Given <code class='latex inline'>f(x) = 7 - 2(x - 1)^2</code>, <code class='latex inline'>x \geq 1</code>, determine <code class='latex inline'> \displaystyle f^{-1}(5) </code></p>
<p>The height of a ball thrown from a balcony can be modelled by the function <code class='latex inline'>h(t) = -5t^2 + 10t + 35</code>, where <code class='latex inline'>h(t)</code> is the height above the ground, in metres, at time <code class='latex inline'>t</code> seconds after its is thrown. </p><p>What are the domain and range of the new model?</p>
<p>Given <code class='latex inline'>f(x) = -(x + 1)^2 -3</code> for <code class='latex inline'>x \geq -1</code>, determine the equation for <code class='latex inline'>f^{-1}(x)</code>. Graph the function and its inverse on the same axes.</p>
<p>The set of ordered pairs defines a parabola. Graph the relation and its inverse. </p><p> {(0, 0), (1, 3), (2, 12), (3, 27)}</p>
<p>Consider <code class='latex inline'>f(x) = -2x^2 + 3x - 1</code>.</p><p>Why were the values of <code class='latex inline'>x</code> restricted in parts (c) and (d)?</p>
<p>Each graph shows a function <code class='latex inline'>f</code> that is a parabola or a branch of a parabola.</p><img src="/qimages/888" /> <ul> <li>i) Determine <code class='latex inline'>f(x)</code></li> <li>ii) Graph <code class='latex inline'>f^{-1}</code></li> <li>iii) State restrictions on the domain or range of <code class='latex inline'>f</code> to make its inverse a function.</li> <li>iv) Determine the equation(s) for <code class='latex inline'>f^{-1}</code>.</li> </ul>
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