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The given problem appears to be a question involving a function \( f(x) \). The exact text is somewhat unclear, but it seems to state the following:

"If \( y = f(x) \) and \( y = 125 \) when \( x = 5 \), find the value of \( x \) when \( y = 27 \)."

Let's solve this step-by-step.

### Step 1: Identify the function \( f(x) \)

From the given information, we know:
\[ f(5) = 125 \]

### Step 2: Assume a possible form of \( f(x) \)

A common form for such problems is a power function, \( f(x) = x^n \). Let's assume:
\[ f(x) = kx^n \]

We can use the given information to find \( k \) and \( n \):
\[ f(5) = 125 \]
\[ k \cdot 5^n = 125 \]

### Step 3: Solve for \( n \)

Assuming \( k = 1 \) (the simplest assumption), then:
\[ 5^n = 125 \]
\[ 5^n = 5^3 \]
Therefore,
\[ n = 3 \]

So the function is:
\[ f(x) = x^3 \]

### Step 4: Find the value of \( x \) when \( y = 27 \)

Now we need to find \( x \) when:
\[ f(x) = 27 \]
\[ x^3 = 27 \]
Taking the cube root of both sides:
\[ x = \sqrt[3]{27} \]
\[ x = 3 \]

So, the value of \( x \) when \( y = 27 \) is:
\[ x = 3 \]

Would you like any additional details or have any questions on this solution?

### Related Questions:

1. How do we determine the form of a function given certain points?
2. What are power functions and how are they used in problem-solving?
3. How do you solve equations involving exponents and roots?
4. Can \( k \) be something other than 1 in the function \( f(x) = kx^n \)?
5. What other types of functions could fit the given points?
6. How would the solution change if the function was logarithmic?
7. How can we verify the solution graphically?
8. What if there are multiple solutions for \( x \) when \( y = 27 \)?

### Tip:
When solving for functions based on given values, consider different forms (polynomials, exponentials, logarithmic, etc.) and verify by plugging back into the original conditions.

Explore how to solve the function problem where y = f(x), and y = 27. Understand the step-by-step solution involving power functions and cube roots. Suitable for high school students.

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