Question

Use algebra to find the inverse of the function f(x)=3x^5+7

Answer 1

Answer:

The inverse of the function is  $f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}$

Step-by-step explanation:

The steps to get the inverse of a function are:

1. Replace f(x) with y
2. Replace every x by y and every y by x
3. Solve the new equation from for y
4. Replace y with $f^{-1}(x)$

∵ $f(x)=3x^{5}+7$

- Replace f(x) by y

∴ $y=3x^{5}+7$

- Replace every x by y and every y by x

∴  $x=3y^{5}+7$

- Subtract 7 from both sides

∴ $x-7=3y^{5}$

- Divide both sides by 3

∴ $\frac{x-7}{3}=y^{5}$

- Insert fifth root for both sides

∴ $\sqrt[5]{\frac{x-7}{3}}=y$

- Switch the two sides

∴ $y=\sqrt[5]{\frac{x-7}{3}}$

- replace y by $f^{-1}(x)$

∴ $f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}$

The inverse of the function is  $f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}$