Question

When f(x) = x-7/2 , what is the value of (f^0 f^-1) (3)

Answer 1

Answer:

$(f o f^{-1})(3) = 3$

Step-by-step explanation:

$f(x) = \frac{x-7}{2}$

We need to find (fof^-1)(3)

First we find f^-1(x)

Replace f(x) with y

$y = \frac{x-7}{2}$

Now replace x  with y and y with x

$x = \frac{y-7}{2}$

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)

$(f o f^{-1})(3) = f(f^{-1}(3))$

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)

$f(x) = \frac{x-7}{2}$

$f(13) = \frac{13-7}{2}= 3$

So , $(f o f^{-1})(3) = f(f^{-1}(3))= 3$