Find the inverse of the function f(x) =[(x-3)/4]^1/4

Expert Answers
hala718 eNotes educator| Certified Educator

f(x) = [(x-3)/4]^1/4

To find the inverse we will assume that:

y= [(x-3)/4]^1/4

Now let y to the 4th power:

y^4= (x-3)/4

Multiply by 4:

4y^4 = x-3

Now add 3:

4y^4 + 3 = x

Then the inverse of the function f(x) is:

f(x)^-1= 4x^4  +3

neela | Student

f(x) = {(x-1)/4}^(1/4)x. To find the inverse.

Solution:

Let y = {(x-3)/4}^(1/4). Taking 4th power we get

y^4 = (x-3)/4. Or

4y^4=(x-3). Or

y^4 +3 = x. Or

x = y^4+3.

Interchanging x and y, we get

y = x^4+3 which is the inverse function.