Question

f(x)=6x-6 and g(x)=1/6(x+6)
What is f(g(x))?
Any given values of x≠?
What is g(x(x))?
Any given values of x≠?
And are the functions of f and g inverses of each other?

Answer 1

i assume this is
\[g(x)=\frac{x+6}{6}\]

Answer 2

so f and g are inverses because
\[f(g(x))=6\times (\frac{x+6}{6})-6=x+6-6=x\]

Answer 3

there are no restrictions on x because both f and g are polynomials

Answer 4

\[g(g(x))=g(\frac{x+6}{6})=\frac{\frac{x+6}{6}+6}{6}\]

Answer 5

a little algebra (muliply top and bottom by 6) gives
\[\frac{x+6+36}{36}=\frac{x+42}{6}\]