91Ó°ÊÓ

For each function, find a domain on which \(f\) is one-to-one and non- decreasing, then find the inverse of \(f\) restricted to that domain. $$ f(x)=(x-6)^{2} $$

Given each function, evaluate: \(f(-1), f(0), f(2), f(4)\). $$ f(x)=\left\\{\begin{array}{lll} 4 x-9 & \text { if } & x<0 \\ 4 x-18 & \text { if } & x \geq 0 \end{array}\right. $$

Sketch a graph of each function as a transformation of a toolkit function. $$ f(t)=(t+1)^{2}-3 $$

For each function, find a domain on which \(f\) is one-to-one and non- decreasing, then find the inverse of \(f\) restricted to that domain. $$ f(x)=x^{2}-5 $$

Given each function, evaluate: \(f(-1), f(0), f(2), f(4)\). $$ f(x)=\left\\{\begin{array}{cll} x^{2}-2 & \text { if } & x<2 \\ 4+|x-5| & \text { if } & x \geq 2 \end{array}\right. $$

Sketch a graph of each function as a transformation of a toolkit function. $$ h(x)=|x-1|+4 $$

Given each function, evaluate: \(f(-1), f(0), f(2), f(4)\). $$ f(x)=\left\\{\begin{array}{lll} 4-x^{3} & \text { if } & x<1 \\ \sqrt{x+1} & \text { if } & x \geq 1 \end{array}\right. $$

For each function, find a domain on which \(f\) is one-to-one and non- decreasing, then find the inverse of \(f\) restricted to that domain. $$ f(x)=x^{2}+1 $$

If \(f(x)=x^{3}-5\) and \(g(x)=\sqrt[3]{x+5},\) find a. \(\quad f(g(x))\) b. \(g(f(x))\) c. What does this tell us about the relationship between \(f(x)\) and \(g(x) ?\)

Given each function, evaluate: \(f(-1), f(0), f(2), f(4)\). $$ f(x)=\left\\{\begin{array}{ccc} 5 x & \text { if } & x<0 \\ 3 & \text { if } & 0 \leq x \leq 3 \\ x^{2} & \text { if } & x>3 \end{array}\right. $$