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The problem in your image asks to find the inverse of the function:

\[
f(x) = \left(\frac{x}{8}\right)^{\frac{1}{7}}
\]

To find the inverse function \( f^{-1}(x) \), we follow these steps:

### Step 1: Set \( y = f(x) \)
\[
y = \left(\frac{x}{8}\right)^{\frac{1}{7}}
\]

### Step 2: Solve for \( x \) in terms of \( y \)
We need to solve for \( x \) from the equation \( y = \left(\frac{x}{8}\right)^{\frac{1}{7}} \).

First, raise both sides of the equation to the power of 7 to eliminate the exponent on the right-hand side:
\[
y^7 = \frac{x}{8}
\]

### Step 3: Multiply both sides by 8 to isolate \( x \):
\[
x = 8y^7
\]

### Step 4: Replace \( y \) with \( x \) to write the inverse function:
\[
f^{-1}(x) = 8x^7
\]

So, the inverse function is:

\[
f^{-1}(x)

For the function f(x) = (x/8)^(1/7), find f^(-1)(x).

This problem demonstrates how to find the inverse of the function f(x) = (x/8)^(1/7) through step-by-step algebraic manipulation. Learn how to isolate variables and apply exponent rules. Suitable for students in Grades 10-12.

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