Question

If f(x)=3x+2 and g^-1(f^-1(x))=5x-4 find g(x)

Answer 1

\(\Large f(x)=3x+2 \rightarrow f^{-1}(x)=\frac{x-2}{3} \)
now let \(\large y=\frac{x-2}{3} \) so that:
\(\Large g^{-1}(f^{-1}(x))=5x-4 \) or \(\Large g^{-1}(y)=5x-4 \)
since \(\large x=3y+2 \),
\(\Large g^{-1}(y)=5x-4 =5(3y+2)-4=15y+10-4=15y+6\)

can you take it from here to find g(x) ??

Answer 2

g(x)=(x-6)/15??????

Answer 3

that should be right... yes...

Answer 4

HECK FREAKING YES!!!!!! THANK YOU SO MUCH.

Answer 5

yw.... :)