Answer:
[tex](g\ o\ f)(x) = -10x^2 + 25x + 44[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x^2 - 5x - 8[/tex]
[tex]g(x) = -5x+4[/tex]
Required
[tex]Find:\ (g\ o\ f)(x)[/tex]
In functions;
[tex](g\ o\ f)(x) = g(f(x))[/tex]
Substitute [tex]f(x) = 2x^2 - 5x - 8[/tex] in [tex](g\ o\ f)(x) = g(f(x))[/tex]
[tex](g\ o\ f)(x) = g(f(2x^2 - 5x - 8))[/tex]
Solving for [tex]g(f(2x^2 - 5x - 8))[/tex]
If [tex]g(x) = -5x+4[/tex]
then
[tex]g(f(2x^2 - 5x - 8)) = -5(2x^2 - 5x - 8) + 4[/tex]
Open Bracket
[tex]g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 40 + 4[/tex]
[tex]g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 44[/tex]
Recall that:
[tex](g\ o\ f)(x) = g(f(2x^2 - 5x - 8))[/tex]
This implies that
[tex](g\ o\ f)(x) = -10x^2 + 25x + 44[/tex]
