Question

F(x)=

Answer 1

Answer:

$(g\ o\ f)(x) = -10x^2 + 25x + 44$

Step-by-step explanation:

Given

$f(x) = 2x^2 - 5x - 8$

$g(x) = -5x+4$

Required

$Find:\ (g\ o\ f)(x)$

In functions;

$(g\ o\ f)(x) = g(f(x))$

Substitute $f(x) = 2x^2 - 5x - 8$ in $(g\ o\ f)(x) = g(f(x))$

$(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))$

Solving for $g(f(2x^2 - 5x - 8))$

If $g(x) = -5x+4$

then

$g(f(2x^2 - 5x - 8)) = -5(2x^2 - 5x - 8) + 4$

Open Bracket

$g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 40 + 4$

$g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 44$

Recall that:

$(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))$

This implies that

$(g\ o\ f)(x) = -10x^2 + 25x + 44$