91Ó°ÊÓ

For the following exercises, find functions \(f(x)\) and \(g(x)\) so the given function can be expressed as \(h(x)=f(g(x))\). \(h(x)=\sqrt{2 x+6}\)

For the following exercises, evaluate or solve, assuming that the function \(f\) is one-to-one. If \(f^{-1}(-4)=-8\), find \(f(-8)\).

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. \(f(x)=x^{4}-4 x^{3}+5\)

For the following exercises, find functions \(f(x)\) and \(g(x)\) so the given function can be expressed as \(h(x)=f(g(x))\). \(h(x)=(5 x-1)^{3}\)

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. \(h(x)=x^{5}+5 x^{4}+10 x^{3}+10 x^{2}-1\)

If possible, find all values of \(a\) such that there are no \(x\) - intercepts for \(f(x)=2|x+1|+a\).

For the following exercises, evaluate or solve, assuming that the function \(f\) is one-to-one. If \(f^{-1}(-2)=-1,\) find \(f(-1)\)

For the following exercises, evaluate the function \(f\) at the indicated values \(f(-3), f(2), f(-a),-f(a), f(a+h)\). Given the function \(p(c)=c^{2}+c:\) (a) Evaluate \(p(-3)\). (b) Solve \(p(c)=2\).

For the following exercises, evaluate the function \(f\) at the indicated values \(f(-3), f(2), f(-a),-f(a), f(a+h)\). Given the function \(f(x)=x^{2}-3 x:\) (a) Evaluate \(f(5)\). (b) Solve \(f(x)=4\).

For the following exercises, use the values listed in to evaluate or solve. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline f(x) & 8 & 0 & 7 & 4 & 2 & 6 & 5 & 3 & 9 & 1 \\ \hline \end{array} $$ Find \(f(1)\).