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

Answer:

[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]

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:

[tex](g\circ f)(x)=g(f(x))[/tex]

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

Given the functions:

[tex]f(x) = 3x^2 - 4x - 1[/tex]

[tex]g(x) = -2x + 5[/tex]

We need to find

[tex](g\circ f)(x)=g(f(x))[/tex]

Replace f into g:

[tex](g\circ f)(x)=-2(3x^2 - 4x - 1) + 5[/tex]

Operating:

[tex](g\circ f)(x)=-6x^2 +8x +2 + 5[/tex]

Reducing:

[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]

Thus,

[tex]\boxed{(g\circ f)(x)=-6x^2 +8x +7}[/tex]

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