Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(1).f(x) = 2x2 – 22 – 4g(x) = 5x = 14

Answer 1

Given:

f(x) = 2x^2-2x-4.

g(x) = -5x+14.

The objective is to find the value of (gof) (1).

The (gof) (x) can be calculated as,

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =-5(2x^2-2x-4)+14 \\ =-10x^2+10x+20+14 \\ =-10x^2+10x+34 \end{gathered}$

Now, substitute x= 1 in the above function.

$\begin{gathered} (g\circ f)(x)=-10(1)^2+10(1)+34 \\ =-10+10+34 \\ =34 \end{gathered}$

Hence, the value of (gof) (1) is 34.