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Delicious77 [7]
3 years ago
15

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

Mathematics
1 answer:
brilliants [131]3 years ago
3 0

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}}

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