Hello!
The answer is:
[tex](g \circ f)(x)=4x^{2}-4x-1[/tex]
Why?
To solve the problem, we need to remember that composing functions means evaluate a function into another different function.
Also, we need to remember how to solve the following notable product:
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
We have that:
[tex](g \circ f)(x)=g(f(x))[/tex]
Now, we are given the equations:
[tex]f(x)=2x-1\\g(x)=x^{2}-2[/tex]
So, composing we have:
[tex](g \circ f)(x)=g(f(x))[/tex]
[tex](g \circ f)(x)=(2x-1)^{2}-2[/tex]
Now, we have to solve the notable product:
[tex](g \circ f)(x)=((2x)^{2}-2(2x*1)+1^{2})-2[/tex]
[tex](g \circ f)(x)=4x^{2}-4x+1-2[/tex]
Hence, we have that:
[tex](g \circ f)(x)=4x^{2}-4x-1[/tex]
Have a nice day!
