Let `f(x)=|x|` Then number of solutions of `f(x)=0 " in"[-2,2]` is

Options

A. 0
B. 1
C. 2
D. 4

Answer

To solve the problem, we need to determine the number of solutions to the equation \( f(x) = 0 \) where \( f(x) = |x| \) in the interval \([-2, 2]\).

### Step-by-Step Solution:

1. **Define the function**: We start with the function \( f(x) = |x| \).

2. **Set the equation**: We need to solve the equation \( |x| = 0 \).

3. **Solve the equation**: The equation \( |x| = 0 \) implies that \( x = 0 \) because the absolute value of a number is zero only when the number itself is zero.

4. **Check the interval**: We need to check if the solution \( x = 0 \) lies within the given interval \([-2, 2]\). Since \( 0 \) is indeed within this interval, it is a valid solution.

5. **Count the solutions**: As we found only one solution, which is \( x = 0 \), we conclude that there is a total of one solution in the interval \([-2, 2]\).

### Final Answer:
The number of solutions of \( f(x) = 0 \) in the interval \([-2, 2]\) is **1**.

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