Question

Calculate g (x) , where g=f-1. State the domain and range of g. Calculate g'(a).

Answer 1

Find \[f ^{-1}(x)\]
Then\[g=f ^{-1}x\]
Then differentiate \[g(x)\]to get \[g'(x)\]

Answer 2

Thats what I have been trying but I keep getting an answer different then the answers. Could you complete the problem?

Answer 3

Let
y=1/(x-5)
y(x-5)=1
xy-5y=1
xy=1+5y
x=(1+5y)/y
\[f ^{-1}(x)=\frac{1+5x}{x}\]
Since \[g=f ^{-1}x\]
\[g(x)=\frac{1+5x}{x}\]
Differentiate g(x)
\[g'(x)=\frac{x(5)-(1+5x)(1)}{x ^{2}}\]
\[g'(x)=\frac{-1}{x ^{2}}\]
when g'(a) and a=3
\[g'(3)=-\frac{1}{(3)^{2}}\]
\[g'(3)=-\frac{1}{9}\]