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

Rewrite with y: To find the inverse function, we need to switch the roles of x and y in the original function and then solve for y. Let's start by rewriting the function with y: f(x) = (x+5)^(1/5) y = (x+5)^(1/5) Now we switch x and y: x = (y+5)^(1/5)Switch x and y: Next, we need to isolate y. To do this, we raise both sides of the equation to the power of 5 to eliminate the exponent on the right side: x^5 = ((y+5)^(1/5))^5 x^5 = y+5Isolate y: Now, we subtract 5 from both sides to solve for y: x^5 - 5 = y y = x^5 - 5Final Inverse Function: We have found the inverse function by solving for y. The inverse function is: f^(-1)(x) = x^5 - 5

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

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

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

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

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

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

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

, find

f^{-1}(x)

\newline

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

\newline

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

\newline

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

\newline

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

Rewrite with y: To find the inverse function, we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by rewriting the function with $y$ :
$f(x) = (x+5)^{\frac{1}{5}}$
$y = (x+5)^{\frac{1}{5}}$
Now we switch $x$ and $y$ :
$x = (y+5)^{\frac{1}{5}}$
Switch x and y: Next, we need to isolate $y$ . To do this, we raise both sides of the equation to the power of $5$ to eliminate the exponent on the right side: $\newline$ $x^5 = ((y+5)^{1/5})^5$ $\newline$ $x^5 = y+5$
Isolate $y$ : Now, we subtract $5$ from both sides to solve for $y$ : $x^5 - 5 = y$ $y = x^5 - 5$
Final Inverse Function: We have found the inverse function by solving for $y$ . The inverse function is: $f^{-1}(x) = x^5 - 5$