Question

F(x)

g(x)
​

=x−5
=
x
2
+4
x
2
−12
​

Write g(f(x))g(f(x))g, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis as an expression in terms of xxx.
g(f(x))=g(f(x))=g, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis, equals

Answer 1

g(f(x)) =
`(x^2-10x+13)/(x^2-10x+29)`

Explanation:

substitute x = f(x) into g(x) , that is

g(f(x))

=
`((x-5)^2-12)/((x-5)^2+4)` ← expand factor (x - 5)² using FOIL

=
`(x^2-10x+25-12)/(x^2-10x+25+4)`

=
`(x^2-10x+13)/(x^2-10x+29)`