Question

Find f^-1(x) for f(x)=1/x^3 and state whether or not it is a function.

Answer 1

To find the inverse of a function, switch the x and y (the f(x) =y) then solve for y.

x = 1/(y^3)

xy^3 = 1

y^3 = 1/x

f^-1(x) = y = 1/x^(1/3)

Note: 1/3 power is the same as cube root.

Yes it is a function

Answer 2

Inverse function is
`f^(-1)=\sqrt[3]{(1)/(x)}`

It is a function

Explanation:

`f(x)= (1)/(x^3)`

Replace f(x) with y

`y= (1)/(x^3)`

Now we replace x with y and y with x

`x= (1)/(y^3)`

Now multiply by y^2 on both sides and solve for y

xy^3 = 1

divide by x on both sides

`y^3= (1)/(x)`

Take cube root on both sides

`y=\sqrt[3]{(1)/(x) }`

Inverse function is
`f^(-1)=\sqrt[3]{(1)/(x)}`

For every value of x there is a y value . for each input there is only one output

so it is a function