If f and g are one-to-one functions where f(-7)=6, F(2)=9 and g(-7)=9, then find-
a)g of f^-1(6)
b)f of g^-1(9)
c)f^-1 of g(-7)
I'm confused as to what goes where? I know how to compose functions, but this is confusing to me?
Remember that when you have inverse functions, the $\displaystyle x$ and $\displaystyle y$ values swap.
So if $\displaystyle f(-7) = 6$ then $\displaystyle f^{-1}(6) = -7$.
If $\displaystyle F(2) = 9$ then $\displaystyle F^{-1}(9) = 2$.
If $\displaystyle g(-7) = 9$ then $\displaystyle g^{-1}(9) = -7$.
So to answer your questions...
a) $\displaystyle g\left(f^{-1}(6)\right) = g(-7) = 9$.
b) $\displaystyle f\left(g^{-1}(9)\right) = f(-7) = 6$.
c) $\displaystyle f^{-1}\left(g(-7)\right) = f^{-1}(9)$.
Since we do not have any information about $\displaystyle f^{-1}(9)$ we can not go any further.