Question

The inverse of the function f(x) = x + 10 is shown.

h(x) = 2x –

What is the missing value?

Answer 1

The Given function is

y= x + 10

To find the inverse of function , we use the following procedure

x=y-10

Now, replace x by y and y by x, we get the inverse of function

y=x -10 , is the inverse of the function, y=x+10.

As, it is given that inverse of f(x) is h(x)

Also, h(x)= 2 x - k-------(1)

Inverse of f(x)=x+10 is ,y= x-10, that is 2 y=2 x- 20------(2)

Comparing 1 and 2, gives

h(x)=2 y

-k=-20

k=20

Answer 2

we have

`f(x) = (1)/(2)x + 10`

Step
`1`

Let

y=f(x)

`y = (1)/(2)x + 10`

Exchange the variable x for y and variable y for x

`x = (1)/(2)y + 10`

Clear variable y

Multiply by
`2` both sides

`2x = y + 20`

`y = 2x-20`

Let

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

`f(x)^(-1)=2x-20`

therefore

the answer is

the inverse of the function is
`f(x)^(-1)=2x-20`

the missing value is
`20`