Question

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

Answer 1

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:

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

Answer 2

Answer:

h(x) = x/2 + 5

Step-by-step 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