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

User Suffii
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Answer:

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

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


(x-7)/(3)=y^(5)

- Insert fifth root for both sides


\sqrt[5]{(x-7)/(3)}=y

- Switch the two sides


y=\sqrt[5]{(x-7)/(3)}

- replace y by
f^(-1)(x)


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

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

User Matthew Spence
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