For each graph shown below, state the solution to each of the following:
\displaystyle
\begin{array}{llllllll}
&(a) \phantom{.} f(x) = g(x)
&(b) \phantom{.} f(x) \leq g(x) \\
&(c) \phantom{.} f(x) > g(x)
&(b) \phantom{.} f(x) \geq g(x) \\
\end{array}
For each graph shown below, state the solution to each of the following:
\displaystyle
\begin{array}{llllllll}
&(a) \phantom{.} f(x) = g(x)
&(b) \phantom{.} f(x) \leq g(x) \\
&(c) \phantom{.} f(x) > g(x)
&(b) \phantom{.} f(x) \geq g(x) \\
\end{array}
Solve for x \in [0, 2]
\displaystyle
3 = 2^{2x}
Solve for x
\displaystyle
0 = \sin(0.25x^2)
when x \in [0, 5]
Solve for x
\displaystyle
3x = 0.5x^3
when x \in [-8, -1]
Solve for x
\displaystyle
\cos x = x
when x \in [0, \frac{\pi}{2}]
Solve for x when
a) f(x) < g(x)
b) f(x) = g(x)
c) f(x) > g(x)
Solve using a graphing device.
Solve the following equations for x in the given interval, using a guess and improvement strategy. Express your answers to the nearest tenth.
\displaystyle
\sin^3x = \sqrt{x} -1, 0 \leq x \leq \pi
Solve for x.
\sin(2\pi x) = -4x^2+ 16x - 12, 0 \leq x \leq 5
Solving inequalities in Composite Functions.
ex. Solve for x for
\displaystyle
\log_2(x + 1) > 2
ex. Solve for x for
\displaystyle
[\log_2(x - 1)]^2 - 2\log_2(x - 1) > 0
ex. Solve for x for
\displaystyle
2^{\log_2(x + 2)}> 27
ex. Solve for x for
\displaystyle
1 \leq \log_2(x^2 - 1) \leq 3
ex. Find the inverse of
\displaystyle
y = 2^{3^{x - 1}} + 3
ex. Find the inverse of
\displaystyle
f(x) = -3\log_3\log_2(x + 5) + 2
and find the range of f(x).