Question

Use f(x) = 1)2 and f^-1(x) = 2x to solve the problems. a) f(2) b)f^-1(1) c)f^-1(f(2))​

Answer 1

a) f (2) = 1

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

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

Explanation:

`f^(-1)` - Indicates that we have to find the inverse of the function

Given data:

`f(x)=\left((1)/(2)\right) x` --------> eq.1

`f^(-1)(x)=2 x` ---------> eq.2

To find
`f(2), f^(-1)(1), f^(-1)(f(2))`

Case a)

Now, substitute x = 2 in the equation 1 to find f (2)

`f(2)=\left((1)/(2)\right) * 2=1`

Case b)

Now, substitute x = 1 in the equation 2 to find
`f^(-1)(1)`

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

Case c)

In general,

`f^(-1)(f(x))=f\left(f^(-1)(x)\right)=x`

Thereby,

`f^(-1)(f(2))=2 \text { where } x=2`