Solution

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


We may evaluate the function at the indicated values by simply replacing each $x$ in $g(x) = x^2 + x + h$ with the corresponding input expression specified in the parentheses:

$$\begin{array}{rclll} g(3) &=& 3^2+3+h &=& 12+h\\ g(h) &=& h^2 + h + h &=& h^2 + 2h\\ g(a+b) &=& (a+b)^2 + (a+b) + h &=& a^2 + 2ab + b^2 + a + b + h\\ g(x+h) &=& (x+h)^2 + (x+h) + h &=& x^2 + 2xh + h^2 + x + 2h \end{array}$$