Question

Find the inverse of f informally. verify that f(f^-1(x))=x and f^-1(f(x))=x f(x)= (x-1)/5

Answer 1

Find inverse function.
$f(x)= \frac{x-1}{5} \\y= \frac{x-1}{5} \\x= \frac{y-1}{5} \\y-1=5x \\y=5x+1 \\f^{-1}(x)=5x+1 \\ \\f(x)= \frac{x-1}{5} \\f^{-1}(x)=5x+1 \\ \\f(f^{-1}(x))=f(5x+1)= \frac{(5x+1)-1}{5} = \frac{5x}{5}= x \\ \\ f^{-1}(f(x))=f^{-1}(\frac{x-1}{5} )=5\frac{x-1}{5}+1=x-1+1=x$