Question

F(x) = 3x2 – 4x – 1 g(x) = –2x + 5 Find: (gof)(x)

Answer 1

Answer:

$(g\circ f)(x)=-6x^2 +8x +7$

Step-by-step explanation:

The Composite Function

Given f(x) and g(x) real functions, the composite function, named (g\circ f)(x) is defined as:

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

For practical purposes, it's found by substituting f into g.

Given the functions:

$f(x) = 3x^2 - 4x - 1$

$g(x) = -2x + 5$

We need to find

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

Replace f into g:

$(g\circ f)(x)=-2(3x^2 - 4x - 1) + 5$

Operating:

$(g\circ f)(x)=-6x^2 +8x +2 + 5$

Reducing:

$(g\circ f)(x)=-6x^2 +8x +7$

Thus,

$\boxed{(g\circ f)(x)=-6x^2 +8x +7}$