Question

Use f(x) = 2 x and f-1(x) = 2x to solve the problems. F^-1(f(x))= f(f^-1(x))

Answer 1

Answer:

see the procedure

Step-by-step explanation:

we have

$f(x)=\frac{1}{2}x$

$f^{-1}(x)=2x$

step 1

Find $f^{-1}(f(x))$

substitute the variable x for the function f(x)

$f^{-1}(f(x))=2(\frac{1}{2}x)$

simplify

$f^{-1}(f(x))=x$

step 2

Find $f(f^{-1}(x))$

substitute the variable x for the function f^-1(x)

$f(f^{-1}(x))=\frac{1}{2}(2x)$

simplify

$f(f^{-1}(x))=x$

step 3

Compare

$f^{-1}(f(x))=x$

$f(f^{-1}(x))=x$

therefore

$f^{-1}(f(x))=f(f^{-1}(x))$ ---> is verified

Answer 2

Answer: the answer is actually X

Step-by-step explanation: