The function of `f` is continuous and has the property `f(f(x))=1-xdot` Then the value of `f(1/4)+f(3/4)` is

Explanation

To solve the problem, we need to find the value of \( f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) \) given the property \( f(f(x)) = 1 - x \).

### Step-by-step Solution:

1. **Understand the given property**: We have the function \( f \) such that \( f(f(x)) = 1 - x \). This means that applying the function \( f \) twice to \( x \) results in \( 1 - x \).

2. **Substitute \( f(x) \)**: Let's replace \( x \) in the original equation with \( f(x) \):
\[ f(f(f(x))) = 1 - f(x) \]
From the original property, we know that \( f(f(x)) = 1 - x \), so we can rewrite this as:
\[ f(1 - x) = 1 - f(x) \]

3. **Evaluate at specific points**: Now, we can use this new relationship to find \( f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) \). Notice that:
\[ f\left(\frac{1}{4}\right) + f\left(1 - \frac{1}{4}\right) = f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) \]
According to our derived relationship:
\[ f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) = 1 \]

4. **Conclusion**: Therefore, we conclude that:
\[ f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) = 1 \]

### Final Answer:
The value of \( f\left(\frac{1}{4}\right) + f\left(\frac{3}{4}\right) \) is \( 1 \).

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