Answer:
[tex](f o f^{-1})(3) = 3[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{x-7}{2}[/tex]
We need to find (fof^-1)(3)
First we find f^-1(x)
Replace f(x) with y
[tex]y = \frac{x-7}{2}[/tex]
Now replace x with y and y with x
[tex]x = \frac{y-7}{2}[/tex]
Multiply by 2 on both sides
2x = y -7
Now add 7 on both sides
2x + 7 = y
Replace y with f^-1(x)
f^-1(x) = 2x+ 7
Now we find (fof^-1)(3)
[tex](f o f^{-1})(3) = f(f^{-1}(3))[/tex]
First we find f^-1(3)
f^-1(x) = 2x+ 7
f^-1(3) = 2(3) + 7 = 6 + 7 = 13
Now we plug in 13 for x and find out f(13)
[tex]f(x) = \frac{x-7}{2}[/tex]
[tex]f(13) = \frac{13-7}{2}= 3[/tex]
So , [tex](f o f^{-1})(3) = f(f^{-1}(3))= 3[/tex]
