If f(x)=secx, then

Options

A. `f(x)=f(-x)`
B. `f((1)/(x))=-f(x)`
C. `f(-x)=-f(x)`
D. `f(x)=f((1)/(x))`

Explanation

To solve the problem, we need to determine the properties of the function \( f(x) = \sec x \). Specifically, we want to check if \( f(x) \) is an even function, which means we need to verify if \( f(x) = f(-x) \).

### Step-by-Step Solution:

1. **Define the Function**:
We start with the function given in the problem:
\[ f(x) = \sec x \]
Recall that the secant function is defined as:
\[ \sec x = \frac{1}{\cos x} \]

2. **Evaluate \( f(-x) \)**:
Next, we need to find \( f(-x) \):
\[ f(-x) = \sec(-x) \]
Using the property of the cosine function, we know that:
\[ \cos(-x) = \cos x \]
Therefore, we can substitute this into our expression for \( f(-x) \):
\[ f(-x) = \sec(-x) = \frac{1}{\cos(-x)} = \frac{1}{\cos x} = \sec x \]

3. **Compare \( f(x) \) and \( f(-x) \)**:
Now we compare \( f(x) \) and \( f(-x) \):
\[ f(-x) = \sec x = f(x) \]
Since \( f(-x) = f(x) \), we conclude that \( f(x) \) is indeed an even function.

4. **Conclusion**:
Therefore, we can state that:
\[ f(x) = \sec x \text{ is an even function.} \]