Answer:
[tex]g(f(x))=3x^2-10x-5[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x-1\\g(x)=3x^2-4x-12\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Therefore, the given composite function g(f(x)) means to substitute function f(x) in place of the x in function g(x):
[tex]\begin{aligned}\implies g(f(x))&=g(x-1)\\& = 3(x-1)^2-4(x-1)-12\\&=3(x-1)(x-1)-4x+4-12\\&=3(x^2-2x+1)-4x-8\\&=3x^2-6x+3-4x-8\\&=3x^2-6x-4x+3-8\\&=3x^2-10x-5\end{aligned}[/tex]
Learn more about composite functions here:
https://brainly.com/question/28010848
