Chapter R.2, Problem 23E

A function f is given by

$f\left(x\right)=\frac{1}{{\left(x+3\right)}^2}$.

This function takes a number x, adds 3, squares the result, and takes the reciprocal of that result.

a. Find $f\left(4\right),f\left(0\right),f\left(a\right),f\left(t+4\right),f\left(x+h\right)$, and $\frac{f\left(x+h\right)-f\left(x\right)}{h}$.

b. Note that f could also be given by

$f\left(x\right)=\frac{1}{x^2+6x+9}$.

Explain what this does to an input number x.