For the function f(x)=(x^((1)/(5)+5))/(7), find f^(-1)(x). f^(-1)(x)=7(x^(5)-5) f^(-1)(x)=7x^(5)-5 f^(-1)(x)=(7x-5)^(5) f^(-1)(x)=(7(x-5))^(5)

Write function as y: To find the inverse function, we first write the function as y = (x^(1/5)+5)/7.Swap x and y: Next, we swap x and y to find the inverse function: x = (y^(1/5)+5)/7.Solve for y: Now, we solve for y. Multiply both sides by 7 to get rid of the denominator: 7x = y^(1/5)+5.Isolate term with y: Subtract 5 from both sides to isolate the term with y: 7x - 5 = y^(1/5).Eliminate fifth root: Raise both sides to the power of 5 to eliminate the fifth root: (7x - 5)^5 = y.Find inverse function: We have found the inverse function: f^(-1)(x) = (7x - 5)^5.

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Find derivatives of using multiple formulae

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Q. For the function

f(x)=\frac{x^{\frac{1}{5}+5}}{7}

, find

f^{-1}(x)

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f^{-1}(x)=7\left(x^{5}-5\right)

\newline

f^{-1}(x)=7 x^{5}-5

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f^{-1}(x)=(7 x-5)^{5}

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f^{-1}(x)=(7(x-5))^{5}

Write function as $y$ : To find the inverse function, we first write the function as $y = \frac{x^{\frac{1}{5}}+5}{7}$ .
Swap x and y: Next, we swap x and y to find the inverse function: $x = \frac{y^{\frac{1}{5}}+5}{7}.$
Solve for y: Now, we solve for y. Multiply both sides by $7$ to get rid of the denominator: $7x = y^{(1/5)}+5$ .
Isolate term with y: Subtract $5$ from both sides to isolate the term with $y$ : $7x - 5 = y^{1/5}$ .
Eliminate fifth root: Raise both sides to the power of $5$ to eliminate the fifth root: $(7x - 5)^5 = y$ .
Find inverse function: We have found the inverse function: $f^{-1}(x) = (7x - 5)^5$ .