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

Original Function: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. The original function is f(x) = 7x^(5), which we can write as y = 7x^(5).Replace y with x: Replace y with x to begin finding the inverse function: x = 7y^(5).Isolate y: Now, solve for y. To do this, we need to isolate y on one side of the equation. Start by dividing both sides by 7: (x/7) = y^(5).Take fifth root: Next, take the fifth root of both sides to solve for y: y = root(5)((x/7)).Write Inverse Function: Now that we have solved for y, we can write the inverse function: f^(-1)(x) = root(5)((x/7)).

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

f^(-1)(x)=7root(5)(x)

f^(-1)(x)=root(5)(((x)/(7)))

f^(-1)(x)=((x)/(7))^(5)

f^(-1)(x)=(root(5)(x))/(7)

For the function $f(x)=7 x^{5}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=7 \sqrt[5]{x}$ $\newline$ $f^{-1}(x)=\sqrt[5]{\left(\frac{x}{7}\right)}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{7}\right)^{5}$ $\newline$ $f^{-1}(x)=\frac{\sqrt[5]{x}}{7}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=7 x^{5}

, find

f^{-1}(x)

\newline

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

\newline

f^{-1}(x)=\sqrt[5]{\left(\frac{x}{7}\right)}

\newline

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

\newline

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

Original Function: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . The original function is $f(x) = 7x^{5}$ , which we can write as $y = 7x^{5}$ .
Replace $y$ with $x$ : Replace $y$ with $x$ to begin finding the inverse function: $x = 7y^{5}$ .
Isolate y: Now, solve for y. To do this, we need to isolate y on one side of the equation. Start by dividing both sides by $7$ : $(x/7) = y^{5}$ .
Take fifth root: Next, take the fifth root of both sides to solve for $y$ : $y = \sqrt[5]{\left(\frac{x}{7}\right)}$ .
Write Inverse Function: Now that we have solved for $y$ , we can write the inverse function: $f^{-1}(x) = \sqrt[5]{\left(\frac{x}{7}\right)}$ .