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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

Respuesta :

absor201

Answer:

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

Option A is correct option.

Step-by-step explanation:

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

For finding inverse of x,

First let:

[tex]y=(x+7)^5[/tex]

Now replace x with y and y with x

[tex]x=(y+7)^5[/tex]

Now, solve for y

Taking 5th square root on both sides

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

Now, replace y with [tex]f^{-1} (x)[/tex]

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

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

Option A is correct option.

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