Question

question
given the definitions of f(x) and g(x) below, find the value of g(f(2)).
f(x) = x - 5
g(x) = x² - 2x + 2

Explanation:

Step1: Calculate f(2)

Substitute \( x = 2 \) into \( f(x)=x - 5 \). So \( f(2)=2 - 5=-3 \).

Step2: Calculate g(f(2))

Now substitute \( x = f(2)=-3 \) into \( g(x)=x^{2}-2x + 2 \).
\( g(-3)=(-3)^{2}-2\times(-3)+2=9 + 6+2=17 \).

Answer:

17