Question

If f(x) =69-15x then f(f^-1(x))

Answer 1

If f(x)=69-15x  then $f(f^{-1}(x))=x$

Given :

$f(x)=69-15x$

Lets find out $f^{-1}(x)$. The steps to find out f inverse are

Replace f(x) by y

$y=69-15x\\Interchange \; the \; variables\\x=69-15y\\solve \; for \; y\\x-69=-15y\\Divide \; by \; -15\\\frac{-x+69}{15} =y\\Replace \;y \;with \; f^{-1}\\f^{-1}=\frac{-x+69}{15}$

Now we find $f(f^{-1}(x))$

Replace inverse function in the place of x in f(x)

$f(f^{-1}(x))=f(\frac{-x+69}{15} )=69-15(\frac{-x+69}{15})=69-(-x+69)=69+x-69=x\\f(f^{-1}(x))=x$

Learn more :

brainly.com/question/11242094