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?

Printable View

- Sep 8th 2009, 06:16 PMChinnie15One to One functions
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? - Sep 8th 2009, 06:25 PMProve It
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. - Sep 8th 2009, 06:31 PMChinnie15
Ok, I think I get it now. Thanks! :)