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

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 Link

lisboa lisboa · Answer 2 · 2019-05-21T08:07:58+02:00

Answer:

Inverse function is [tex]f^{-1}=\sqrt[3]{\frac{1}{x}}[/tex]

It is a function

Step-by-step explanation:

[tex]f(x)= \frac{1}{x^3}[/tex]

Replace f(x) with y

[tex]y= \frac{1}{x^3}[/tex]

Now we replace x with y and y with x

[tex]x= \frac{1}{y^3}[/tex]

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

xy^3 = 1

divide by x on both sides

[tex]y^3= \frac{1}{x}[/tex]

Take cube root on both sides

[tex]y=\sqrt[3]{\frac{1}{x} }[/tex]

Inverse function is [tex]f^{-1}=\sqrt[3]{\frac{1}{x}}[/tex]

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

so it is a function