Question

For f(x) = 2x+1 and g(x) = x² − 7, find (f+ g)(x).

Answer 1

Given the functions:

`\begin{gathered} f(x)=2x+1 \\ \\ g(x)=x^2-7 \end{gathered}`

By definition, (f+g)(x) is equivalent to:

`(f+g)(x)=f(x)+g(x)`

Finally, using the expressions for f and g:

`\begin{gathered} f(x)+g(x)=2x+1+x^2-7 \\ \\ \therefore(f+g)(x)=x^2+2x-6 \end{gathered}`