For the function f(x)=x^(5)+6, find f^(-1)(x). f^(-1)(x)=root(5)(x)+6 f^(-1)(x)=root(5)(x)-6 f^(-1)(x)=root(5)(x+6) f^(-1)(x)=root(5)(x-6)

Replace with y: To find the inverse function, f^(-1)(x), we need to replace f(x) with y and solve for x in terms of y. So, we start with y = x^5 + 6.Isolate x: Next, we need to isolate x on one side of the equation. To do this, we subtract 6 from both sides of the equation to get y - 6 = x^5.Take fifth root: Now, we take the fifth root of both sides to solve for x. This gives us x = (y - 6)^(1/5).Express inverse function: Finally, we replace y with f^(-1)(x) to express the inverse function. So, f^(-1)(x) = (x - 6)^(1/5).

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For the function
f(x)=x^(5)+6, find
f^(-1)(x).

f^(-1)(x)=root(5)(x)+6

f^(-1)(x)=root(5)(x)-6

f^(-1)(x)=root(5)(x+6)

f^(-1)(x)=root(5)(x-6)

For the function $f(x)=x^{5}+6$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=\sqrt[5]{x}+6$ $\newline$ $f^{-1}(x)=\sqrt[5]{x}-6$ $\newline$ $f^{-1}(x)=\sqrt[5]{x+6}$ $\newline$ $f^{-1}(x)=\sqrt[5]{x-6}$

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Q. For the function

f(x)=x^{5}+6

, find

f^{-1}(x)

\newline

f^{-1}(x)=\sqrt[5]{x}+6

\newline

f^{-1}(x)=\sqrt[5]{x}-6

\newline

f^{-1}(x)=\sqrt[5]{x+6}

\newline

f^{-1}(x)=\sqrt[5]{x-6}

Replace with $y$ : To find the inverse function, $f^{-1}(x)$ , we need to replace $f(x)$ with $y$ and solve for $x$ in terms of $y$ . So, we start with $y = x^5 + 6$ .
Isolate $x$ : Next, we need to isolate $x$ on one side of the equation. To do this, we subtract $6$ from both sides of the equation to get $y - 6 = x^5$ .
Take fifth root: Now, we take the fifth root of both sides to solve for $x$ . This gives us $x = (y - 6)^{\frac{1}{5}}$ .
Express inverse function: Finally, we replace $y$ with $f^{-1}(x)$ to express the inverse function. So, $f^{-1}(x) = (x - 6)^{\frac{1}{5}}$ .