Answer:
The inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]
Step-by-step explanation:
Inverse of a function:
To find the inverse of a function [tex]y = f(x)[/tex], basically, we have to reverse r. We exchange y and x in their positions, and then we have to isolate y.
In your exercise:
[tex]y = \sqrt[3]{x} - 8[/tex]
Exchanging x and y, we have:
[tex]x = \sqrt[3]{y} - 8[/tex]
[tex]x + 8 = \sqrt[3]{y}[/tex]
Now we have to write y in function of x
[tex](x+8)^{3} = (\sqrt[3]{y})^{3}[/tex]
[tex]y = (x+8)^{3}[/tex]
So, the inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]
