For the function f(x)=((x-1)/(2))^(5), find f^(-1)(x). f^(-1)(x)=2root(5)(x)+1 f^(-1)(x)=2root(5)(x+1) f^(-1)(x)=root(5)(2(x+1)) f^(-1)(x)=root(5)(2x)+1

Define function f(x): Let's start by defining the function f(x) and setting it equal to y for convenience: f(x) = ((x-1)/2)^5 y = ((x-1)/2)^5 Now, to find the inverse function, we need to solve for x in terms of y.Swap x and y: Swap x and y to begin finding the inverse function: x = ((y-1)/2)^5 Now we need to solve for y.Take fifth root: Take the fifth root of both sides to eliminate the exponent on the right-hand side: root(5)(x) = (y-1)/2Multiply by 2: Multiply both sides by 2 to isolate the term with y: 2 * root(5)(x) = y - 1Add 1: Add 1 to both sides to solve for y: 2 * root(5)(x) + 1 = yInverse function in terms of y: Now we have the inverse function in terms of y: f^(-1)(x) = 2 * root(5)(x) + 1

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Q. For the function

f(x)=\left(\frac{x-1}{2}\right)^{5}

, find

f^{-1}(x)

\newline

f^{-1}(x)=2 \sqrt[5]{x}+1

\newline

f^{-1}(x)=2 \sqrt[5]{x+1}

\newline

f^{-1}(x)=\sqrt[5]{2(x+1)}

\newline

f^{-1}(x)=\sqrt[5]{2 x}+1

Define function $f(x)$ : Let's start by defining the function $f(x)$ and setting it equal to $y$ for convenience: $\newline$ $f(x) = \left(\frac{x-1}{2}\right)^5$ $\newline$ $y = \left(\frac{x-1}{2}\right)^5$ $\newline$ Now, to find the inverse function, we need to solve for $x$ in terms of $y$ .
Swap $x$ and $y$ : Swap $x$ and $y$ to begin finding the inverse function: $\newline$ $x = \left(\frac{y-1}{2}\right)^5$ $\newline$ Now we need to solve for $y$ .
Take fifth root: Take the fifth root of both sides to eliminate the exponent on the right-hand side: $\newline$ $\sqrt[5]{x} = \frac{y-1}{2}$
Multiply by $2$ : Multiply both sides by $2$ to isolate the term with $y$ : $2 \times \sqrt[5]{x} = y - 1$
Add $1$ : Add $1$ to both sides to solve for y: $\newline$ $2 \cdot \sqrt[5]{x} + 1 = y$
Inverse function in terms of y: Now we have the inverse function in terms of y: $f^{-1}(x) = 2 \cdot \sqrt[5]{x} + 1$