Question

For which values of x is g(x) greater than f(x) f(x)=-x^2+10x+24 and g(x)=2x+4

Answer 1

Explanation:

The functions are given below as

$\begin{gathered} f(x)=-x^2+10x+24 \\ g(x)=2x+4 \end{gathered}$

To find the values of x for which

$\begin{gathered} g(x)>f(x) \\ 2x+4>-x^2+10x+24 \end{gathered}$

By rewriting in standard form,we will have

$\begin{gathered} 2x+4\gt-x^{2}+10x+24 \\ x^2+2x-10x+4-24>0 \\ x^2-8x-20>0 \end{gathered}$

By factorization, we will have