Answer:
[tex](g\circ f)(x)=2x^2-7[/tex]
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=x^2-1\text{ and } g(x)=2x-5[/tex]
And we want to find:
[tex](g\circ f)(x)[/tex]
This is the same as:
[tex]=g(f(x))[/tex]
So, substitute f(x) into g(x). Thus:
[tex]g(x)=2x-5\\g(f(x))=2(x^2-1)-5[/tex]
Distribute the 2:
[tex]g(f(x))=2x^2-2-5[/tex]
Subtract:
[tex]g(f(x))=2x^2-7[/tex]
Therefore:
[tex](g\circ f)(x)=2x^2-7[/tex]
And we're done!
