Question

If f(x)=2x-5 and g(x)=(1+3x)/(5-2x)

compute g(f^-1(z))

Answer 1

well first solve y=2x-5
for x

Answer 2

y=(x+5)/2

Answer 3

cool \[f^{-1}(x)=\frac{x+5}{2} \\ \text{ so } f^{-1}(z)=\frac{z+5}{2}\]

Answer 4

\[g(\frac{z+5}{2})=?\]

Answer 5

just replace all of those x's in that g thingy with (z+5)/2

Answer 6

i got 17+3z/(-2z)

Answer 7

\[\frac{1+3\frac{z+5}{2}}{5-2 \frac{z+5}{2}} \\ \frac{1+\frac{3(z+5)}{2}}{5-(z+5)} \\ \frac{1+\frac{3(z+5)}{2}}{5-z-5}\]
did you get that far?

Answer 8

\[\frac{1+\frac{3(z+5)}{2}}{-z}\]
yep what you have seems right
good job

Answer 9

thanks again