Chapter R.2, Problem 24E

A function f is given by

$f\left(x\right)=\frac{1}{{\left(x-5\right)}^2}$.

This function takes a number x, subtracts 5 from it, squares the result, and takes the reciprocal of the square.

a. Find $f\left(3\right),f\left(-1\right),f\left(k\right),f\left(t-1\right),f\left(t-4\right)$, and $f\left(x+h\right)$.

b. Note that f could also be given by

$f\left(x\right)=\frac{1}{x^2-10x+25}$.

Explain what this does to an input number x.