Question

What is the inverse of the function f(x) = 2x – 10?

h(x) = 2x – 5
h(x) = 2x + 5
h(x) = one-halfx – 5
h(x) = one-halfx + 5

Answer 1

`h(x)=(x)/(2)+5`

Explanation:

You are given the function
`f(x)=2x-10`. To find the inverse function
`f^(-1)(x)` do such steps:

1. Rewrite the function f(x) as

`y=2x-10`

2. Express x in terms of y:

`y+10=2x\\ \\x=(y)/(2)+5`

3. Change x into y and y into x:

`y=(x)/(2)+5`

Now, the inverse function is

`f^(-1)(x)=(x)/(2)+5`

Answer 2

Option D.

Explanation:

The given function is

`f(x)=2x-10`

We need to find the inverse of the function f(x).

Step 1 : Substitute f(x)=y.

`y=2x-10`

Step 2: Interchange x and y.

`x=2y-10`

Step 3: Isolate variable y.

`x+10=2y`

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

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

`(x)/(2)+5=y`

`y=(x)/(2)+5`

Step 4: Substitute y=h(x).

`h(x)=(1)/(2)x+5`

The inverse of the function f(x) is
`h(x)=(1)/(2)x+5`.

Therefore, the correct option is D.