One way is to solve for the inverse of the first function
remember, to solve, replace f(x) or g(x) with y, switch x and y, solve for y and replace it with [tex]f^{-1} (x)[/tex]
A.
[tex]f(x)=x/2+8\\y=x/2+8\\x=y/2+8\\x-8=y/2[/tex]
[tex]2x-16=y[/tex]
[tex]f^{-1}=2x-16[/tex]
nope, not A
What is the inverse function?
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by [tex]{\displaystyle f^{-1}.}[/tex]
B.
[tex]f(x)=3x^3+16\\y=3x^3+16x=3y^3+16\\x-16=3y^3\\(x-16)/3=y^3[/tex]
[tex]f^{-1}(x)=\sqrt[3]{((x-16)/3)}[/tex]
nope, not the same
not B
C.
[tex]f(x)=18/x-9\\y=18/x-9\\x=18/y-9\\x+9=18/y\\y(x+9)=18\\y=18/(x+9)\\f^{-1}(x)=18/(x+9)[/tex]
The correct, answer is C.
To learn more about the inverse function visit:
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