Question

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

Answer 1

Answer:

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

$f(x) = \frac{1}{2}x + 10$

Step $1$

Let

y=f(x)

$y = \frac{1}{2}x + 10$

Exchange the variable x for y and variable y for x

$x = \frac{1}{2}y + 10$

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 $20$