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

a: f^{-1}(x)=\sqrt[5]{x}+7f −1(x)=5x +7
b: f^−1(x)=x 5 −7
c: f −1(x)=5sqrtx−7
d: f ^−1(x)= 5sqrtx​−7

1 Answer

2 votes

Answer:

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

Option A is correct option.

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.

User Hoshi
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