Question

Find the inverse function of g(x) = 2x + 4. g -1(x) = 4x + 2 g -1(x) = 2x + g -1(x) = x - 2 g -1(x) = 2x - 4

Answer 1

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

Explanation:

the inverse function of g(x) = 2x + 4

To find the inverse of a function we replace g(x) with y

`y=2x+4`

Replace x with y and y with x

`x=2y+4`

Solve the equation for y

Subtract 4 from both sides

`x-4= 2y`

Divide both sides by 2

`(x)/(2) -2=y`

`y=(x)/(2) -2`

Replace y with f inverse

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

Answer 2

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

`g (x) = 2x + 4`

Replace g(x) with y:

`y = 2x + 4`

We exchange the variables:

`x = 2y + 4`

We solve for "y":

We subtract 4 on both sides of the equation:

`x-4 = 2y`

We divide between 2 on both sides of the equation:

`y = \frac {x} {2} -2`

We change y by
`g ^ {-1} (x)`:

`g ^ {- 1} (x) = \frac {x} {2} -2`

Answer:

`g ^ {- 1} (x) = \frac {x} {2} -2`