Question

Given f(x) = 2x - 2/4 the quantity of 2x minus 2 divided by 4, solve for f−1(3).

Answer 1

The answer is that f-1(3) = 7.

In order to find the answer, we first must find the inverse function. The f-1 indicates that we are looking for an inverse. To find any inverse, we first must switch the x and f(x) values. We then solve for the new f(x), which gives us the inverse.

f(x) = (2x - 2)/4 ----> Switch x and f(x)

x = (2f(x) - 2)/4 -----> Multiply both sides by 4

4x = 2f(x) - 2 ----0-> Add 2 to both sides

4x + 2 = 2f(x) ------> Divide both sides by 2

f-1(x) = (4x + 2)/2

Now that we have the inverse function, we can put in 3 and find the answer.

f-1(x) = (4x + 2)/2

f-1(3) = (4(3) + 2)/2

f-1(3) = (12 + 2)/2

f-1(3) = (14)/2

f-1(3) = 7