Question

Given f(x) =5x-6 and g(x)=x-4 find f^-1 of g^-1

Answer 1

Answer:

$f^{-1}(g^{-1}(x))=\dfrac{1}{5}x+2.$

Step-by-step explanation:

1. If $g(x)=x-4,$ then

$y=x-4,\\ \\x=y+4.$

Change y into x and x into y:

$y=x+4,\\ \\g^{-1}(x)=x+4.$

2. If $f(x)=5x-6,$ then

$y=5x-6,\\ \\5x=y+6,\\ \\x=\dfrac{y+6}{5}.$

Change y into x and x into y:

$y=\dfrac{x+6}{5},\\ \\f^{-1}(x)=\dfrac{x+6}{5}.$

3. Find $f^{-1}(g^{-1}(x)):$

$f^{-1}(g^{-1}(x))=f^{-1}(x+4)=\dfrac{(x+4)+6}{5}=\dfrac{x+10}{5}=\dfrac{1}{5}x+2.$