Question

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

Oh(x) = 2х – 5
Oh(x) = 2х + 5
h(x) = -
-
Ch(x) =-

Answer 1

h(x) = x/2 + 5

Explanation:

f(x) = 2x - 10

Step 1. Replace f(x) with y.

y = 2x - 10

Step 2. Switch variables x and y.

x = 2y - 10

Step 3. Solve for y.

2y - 10 = x

2y = x + 10

y = x/2 + 5

Step 4. Replace y with h(x)

h(x) = x/2 + 5

Answer 2

For this case we must find the inverse of the following function:

`f (x) = 2x-10`

For it:

We change
`f (x)` by y:

`y = 2x-10`

We exchange the variables:

`x = 2y-10`

We clear the value of the variable "and":

`x + 10 = 2y\\y = \frac {x + 10} {2}\\y = \frac {x} {2} + \frac {10} {2}\\y = \frac {x} {2} +5`

We change y for
`f^(-1)(x)`:

`f ^(-1)(x) = \frac {x} {2} +5`

Answer:

`f ^ {- 1 }(x) = \frac {x} {2} +5`