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Savatey [412]
3 years ago
14

For the funtion f(x)= (x+7)^5, Find f^-1 (x)

Mathematics
1 answer:
quester [9]3 years ago
6 0

Answer:

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

Option A is correct option.

Step-by-step explanation:

For the function f(x)= (x+7)^5, Find f^{-1} (x)

For finding inverse of x,

First let:

y=(x+7)^5

Now replace x with y and y with x

x=(y+7)^5

Now, solve for y

Taking 5th square root on both sides

\sqrt[5]{x}=\sqrt[5]{(y+7)^5}\\\sqrt[5]{x}=y+7\\=> y+7=\sqrt[5]{x}\\y=\sqrt[5]{x}-7

Now, replace y with f^{-1} (x)

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

So, the inverse of function f(x)= (x+7)^5 is \mathbf{f^{-1} (x)=\sqrt[5]{x}+7}

Option A is correct option.

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