Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\frac{x+11}{6}=f^{-1}(x)^5$

Take the fifth root of each side:

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

And we're done :)

Answer 2

Answer:

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

Step-by-step explanation:

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

Let y equal the equation

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