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Question 11 of 11, Step 1 of 1
Find a formula for the inverse of the following function, if possible.

s(x)=5root(5)(x)+5

Question $11$ of $11$ , Step $1$ of $1$ $\newline$ Find a formula for the inverse of the following function, if possible. $\newline$ $s(x)=5 \sqrt[5]{x}+5$

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Evaluate explicit formulas for sequences

Full solution

Q. Question

11

of

11

, Step

1

of

1

\newline

Find a formula for the inverse of the following function, if possible.

\newline

s(x)=5 \sqrt[5]{x}+5

Replace with $y$ : To find the inverse of the function $s(x) = 5\sqrt{5}(x) + 5$ , we need to express $x$ in terms of $s(x)$ . Let's start by replacing $s(x)$ with $y$ to make the algebra clearer. $\newline$ $y = 5\sqrt{5}(x) + 5$
Isolate $x$ : Next, we need to isolate the term containing $x$ on one side of the equation. To do this, we subtract $5$ from both sides of the equation. $\newline$ $y - 5 = 5\sqrt{5}(x)$
Eliminate coefficient: Now, we need to eliminate the coefficient of the $5^{\text{th}}$ root. We do this by dividing both sides of the equation by $5$ . $\frac{y - 5}{5} = \sqrt{5}(x)$
Remove $5$ th root: To remove the $5$ th root, we raise both sides of the equation to the power of $5$ . $\left(\frac{y - 5}{5}\right)^5 = x$
Express $x$ in terms of $y$ : We have now expressed $x$ in terms of $y$ . The inverse function is found by swapping $x$ and $y$ . So the inverse function, denoted as $s^{-1}(x)$ , is: $\newline$ $s^{-1}(x) = \left(\frac{x - 5}{5}\right)^5$

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