Question

Use f(x) = 1

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

f(2) =

f−1(1) =

f−1(f(2)) =

Answer 1

f(2) = 1

f−1(1) = 2

f−1(f(2)) = 2

Explanation:

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Answer 2

Part 1)
`f(2)=1`

Part 2)
`f^(-1)(1)=2`

part 3)
`f^(-1)(f(2))=2`

Explanation:

we have that

`f(x)=(1)/(2)x`

`f^(-1)(x)=2x`

Part 1) Find f(2)

For x=2

substitute the value of x in f(x)

`f(2)=(1)/(2)(2)`

`f(2)=1`

Part 2) find
`f^(-1)(1)`

For x=1

Substitute the value of x in
`f^(-1)(x)`

`f^(-1)(1)=2(1)`

`f^(-1)(1)=2`

Part 3) Find
`f^(-1)(f(2))`

we know that

`f(2)=1` -----> see part 1)

so

`f^(-1)(f(2))=f^(-1)(1)`

we have that

`f^(-1)(1)=2` -----> see part 2)

therefore

`f^(-1)(f(2))=2`