Question

For f(x)=1/x-2 and g(x)=x^2+3
a.) (f o g)(x)
b.) (g o f)(8)

The work I did for this was wrong, can someone walk me through how to do this right?

Answer 1

a) \(f(g(x)) \implies \ f(x^2+3)\) so \[f(g(x))=\frac{1}{(x^2+3)-2}\]

Answer 2

b) g(f(8)) --> \(\left(\frac{1}{x-2}\right)^2 +3\)

Answer 3

For (a) all you have to do is simplify the denominator, and you'll have your answer :)

Answer 4

for (b) you have \(\left(\frac{1}{x-2}\right)^2 \implies \frac{1}{(x-2)^2} \implies \frac{1}{x^2 -4x+4} \)

Answer 5

Thank yhu! c: I can see where I went wrong.
Thank yhu so much

Answer 6

No problem :)