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barxatty [35]
3 years ago
5

Find the inverse of the function f(x) = x3 + 5

Mathematics
1 answer:
user100 [1]3 years ago
8 0

Answer:

<h2>{f}^{ - 1} (x) =  \sqrt[3]{x - 5}</h2>

Step-by-step explanation:

f(x) =  {x}^{3}  + 5

To find the inverse of f (x) , equate f(x) to y

That's

y = f(x)

y =  {x}^{3}  + 5

<u>Next interchange the terms</u>

That's x becomes y and y becomes x

x =  {y}^{3}  + 5

<u>Next solve for y</u>

<u>Send 5 to the other side of the equation</u>

{y}^{3}  = x - 5

Find the cube root of both sides to make y stand alone

That's

\sqrt[3]{ {y}^{3} }  =  \sqrt[3]{x - 5}

y =  \sqrt[3]{x - 5}

We have the final answer as

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

Hope this helps you

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