Question

What is the inverse of 70x^(3/4)
Please explain each step.

Answer 1

\[
y = 70x^{3/4} \\
\text{Solve for x:} \\
\text{Divide by 70:} \\
\frac{y}{70} = x^{3/4} \\
\text{Raise both sides to 4/3:} \\
??
\]

Answer 2

Does it matter if you switch the x and why first withing the function, because I noticed that you didn't.

Answer 3

You can do it at the beginning or at the end. You will get the same result.

Answer 4

why did you raise it to the 4/3 power and how does it cancel out the ^3/4

Answer 5

Yeah it doesn't really matter, but I like to do this...

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 6

Cancels the right side exponent

Answer 7

\[
(x^{3/4})^{4/3} = x^1 = x
\]

Answer 8

Go aum! :D

Answer 9

Ok so now i understand that, would the answer be----
(x^4/3)/70^4/3

Answer 10

\[
y = 70x^{3/4} \\
\text{Switch x and y:} \\
x = 70y^{3/4} \\
\text{Solve for y:} \\
\text{Divide by 70:} \\
\frac{x}{70} = y^{3/4} \\
\text{Raise both sides to 4/3:} \\
\left(\frac{x}{70}\right)^{4/3} = (y^{3/4})^{4/3} = y^{3/4*4/3} = y^1 = y \\
y = \left(\frac{x}{70}\right)^{4/3} \\
f^{-1}(x) = \left(\frac{x}{70}\right)^{4/3}
\]

Answer 11

OK THANKS SO MUCH AUM!!! I understand. :D

Answer 12

You are welcome.