91Ó°ÊÓ

Solve the following equations. $$\tan x=1$$

Find the inverse function (on the given interval, if specified) and graph both fand \(f^{-1}\) on the same set of axes. Check your work by looking for the required symmetry in the graphs. $$f(x)=x^{2}-2 x+6, \text { for } x \geq 1$$

Find possible choices for the outer and inner functions \(f\) and \(g\) such that the given function \(h\) equals \(f \circ g .\) Give the domain of \(h\). $$h(x)=\frac{2}{\left(x^{6}+x^{2}+1\right)^{2}}$$

Solve the following equations. $$2 \theta \cos \theta+\theta=0$$

Find possible choices for the outer and inner functions \(f\) and \(g\) such that the given function \(h\) equals \(f \circ g .\) Give the domain of \(h\). $$h(x)=\sqrt{x^{4}+2}$$

Solve the following equations. $$\sin ^{2} \theta=\frac{1}{4}, 0 \leq \theta<2 \pi$$

Find possible choices for the outer and inner functions \(f\) and \(g\) such that the given function \(h\) equals \(f \circ g .\) Give the domain of \(h\). $$h(x)=\frac{1}{\sqrt{x^{3}-1}}$$

Let \(A(x)\) be the area of the region bounded by the \(t\) -axis and the graph of \(y=f(t)\) from \(t=0\) to \(t=x\). Consider the following functions and graphs. a. Find \(A(2)\) b. Find \(A(6)\) c. Find a formula for \(A(x)\) $$f(t)=\frac{t}{2}$$.

Solve the following equations. $$\cos ^{2} \theta=\frac{1}{2}, 0 \leq \theta<2 \pi$$

Solve the following equations. $$\sqrt{2} \sin x-1=0$$