Answer:
[tex]f ^{-1} (8) = \frac{3}{2}[/tex]
Step-by-step explanation:
We know the function [tex]f(x)[/tex]
[tex]f (x) = 2x +5[/tex]
We want to find
[tex]f ^{-1} (8)[/tex]
Remember that if we have a function [tex]f(x)[/tex] and its inverse [tex]f ^ {-1}(x)[/tex], then the domain of the function [tex]f^{-1}(x)[/tex] will be the range of the function [tex]f(x)[/tex].
This means that to find [tex]f ^ {-1}(8)[/tex] we must look for:
[tex]f (x) = 2x +5 = 8[/tex]
We solve the equation for x.
[tex]2x + 5 = 8\\\\2x = 8-5\\\\2x = 3\\\\x = \frac{3}{2}[/tex]
So:
[tex]f ^{-1} (8) = \frac{3}{2}[/tex]
