Question

Find the inverse of f(x)=6x^5-11

Answer 1

`f^-^1(x)=\sqrt[5]{(x+11)/(6) }`

Explanation:

`f(x)=6x^5-11\\`

Let y equal the equation

`y =6x^5-11\\y+11=6x^5\\\\Divide\:both\:sides\:of\:the\:equation\:by \: 6\\(y+11)/(6) = (6x^5)/(6) \\\\(y+11)/(6) = x^5\\ \\Quatric\:root\:both\:sides\\\sqrt[5]{(y+11)/(6) } = \sqrt[5]{x^5} \\\\\sqrt[5]{(y+11)/(6) } = x\\\\f^-^1(x) = \sqrt[5]{(x+11)/(6) }`

Answer 2

`f^(-1)(x)=\sqrt[5]{(x+11)/(6)}`

Explanation:

So we have the function:

`f(x)=6x^5-11`

To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for f⁻¹(x). So:

`f(x)=6x^5-11\\x=6(f^(-1)(x))^5-11`

Add 11 to both sides:

`x+11=6(f^(-1)(x))^5`

Divide both sides by 6:

`(x+11)/(6)=f^(-1)(x)^5`

Take the fifth root of each side:

`f^(-1)(x)=\sqrt[5]{(x+11)/(6)}`

And we're done :)