Questions: Find a formula for the inverse of the function. y=(8+sqrt[5]x)^9

Transcript text: Find a formula for the inverse of the function. \[ y=(8+\sqrt[5]{x})^{9} \]

Solution

Step 1: Rewrite the Function

We start with the function given by \( y = (8 + \sqrt[5]{x})^9 \). To find the inverse, we need to express \( x \) in terms of \( y \).

Step 2: Isolate the Radical

Taking the ninth root of both sides, we have: \[ \sqrt[9]{y} = 8 + \sqrt[5]{x} \]

Step 3: Solve for \( \sqrt[5]{x} \)

Next, we isolate \( \sqrt[5]{x} \): \[ \sqrt[5]{x} = \sqrt[9]{y} - 8 \]

Step 4: Eliminate the Radical

To solve for \( x \), we raise both sides to the fifth power: \[ x = \left(\sqrt[9]{y} - 8\right)^5 \]

Thus, the formula for the inverse of the function is: \[ \boxed{x = \left(\sqrt[9]{y} - 8\right)^5} \]

Was this solution helpful?

Unhelpful

Helpful

Next >