Question

Given the function f(x) = 4(x+3) − 5, solve for the inverse function when x = 3.

Answer 1

The inverse function gives us -1 when x = 3.

In order to find this, we have to solve for the inverse. We do this by switching the x and f(x) values and then you can solve for the new f(x) value. The work for this is done below.

f(x) = 4(x + 3) - 5 ----> Switch the x and f(x)

x = 4(f(x) + 3) - 5-----> Add 5 to both sides.

x + 5 = 4(f(x) + 3) ----> Divide both sides by 4.

`(x+5)/(4)` = f(x) + 3 ---> Subtract 3 from both sides.

`(x+5)/(4)` - 3 = f(x)

Now that you've returned to f(x), you have the inverse. Now we can take the inverse equation and plug in for x = 3.

f(x) =
`(x+5)/(4)` - 3

f(3) =
`(3+5)/(4)` - 3

f(3) =
`(8)/(4)` - 3

f(3) = 2-3

f(3) = -1