Question

Consider the following functions.f(x) = x + 5g(x) = 2x − 1Use the functions to find (g ∘ f)−1.

Answer 1

According to the definition,

`(g\circ f)(x)=g(f(x))`

find the composition

`\begin{gathered} g(f(x))=2(x+5)-1 \\ g(f(x))=2x+10-1 \\ g(f(x))=2x+9 \end{gathered}`

then, find the inverse of the function,

`\begin{gathered} y=2x+9 \\ switch\text{ }the\text{ }variables \\ x=2y+9 \\ clear\text{ }for\text{ }y \\ x-9=2y \\ y=(x-9)/(2) \end{gathered}`

Answer:

`(g\circ f)^(-1)=(x-9)/(2)`