how would be find the answer to f(g(x)) when f(x)=2x-12 , g(x)=x^2+2x+4, f(x)=-3/2x-6

Question

f(x)=2x-12 , g(x)=x²+2x+4, f(x)=-3/2x-6

Answer 1

Composition of two functions is easy.  f(g(x) tells you to put g(x) everywhere that x appears, in f(x).

So write down f(x) PUTTING OPEN PARENTHESES INSTEAD OF EVERY x ON THE RIGHT SIDE:

 

f(x) = 2( ) - 12

 

AND NOW GO BACK THERE AND PUT the right side of the expression for g(x) into each EMPTY ( )

 

You now have f(g(x)) = 2(x²+2x+4) - 12.  You can simplify this.

 

In this explanation I have ignored the awkward fact that you stuck on an extra f(x) at the end of your submission.