Solution

Suppose $f(x) = x^3$ for all real values $x$, and then find $f(2)$,  $f(-3)$,  $f(a)$,  $f(b+h)$,  and  $f(x+h)$.


We may evaluate the function at the indicated values by simply replacing each $x$ in $f(x) = x^3$ with the corresponding input expression specified in the parentheses (even if the input expression has an $x$ in it, as seen in the last equation below):

$$\begin{array}{rclll} f(2) &=& 2^3 &=& 8\\ f(-3) &=& (-3)^3 &=& -27\\ f(a) &=& a^3\\ f(b+h) &=& (b+h)^3 &=& b^3 + 3b^2h + 3bh^2 + h^3\\ f(x+h) &=& (x+h)^3 &=& x^3 + 3x^2h + 3xh^2 + h^3 \end{array}$$