Respuesta :

amathzing
To find the inverse all you do is switch the x and y and rewrite the equation.

So if our original equation is y = x^3 - 8, then switch the x and y

x = y^3 - 8 .... and now solve for y

x + 8 = y^3

y = cube root (x + 8), or you can write it as y = (x + 8)^ (1/3)

Answer:

[tex]f^{-1}(x)=\sqrt[3]{x+8}[/tex]

Step-by-step explanation:

[tex]f(x) = x^3 - 8[/tex]

To get inverse function , follow the steps

Replace f(x) by y

[tex]y = x^3 - 8[/tex]

Swap the variables x and y. Replace x with y and y with x

[tex]x= y^3 - 8[/tex], solve the equation for y

Add 8 on both sides

[tex]x+8= y^3[/tex]

To remove cube , take cube root on both sides

[tex]\sqrt[3]{x+8} =y[/tex]

Now replace y with f inverse

[tex]\sqrt[3]{x+8} =f^{-1}(x)[/tex]