Harsh made a piggy bank for himself using clay . If the shape of the bank is based on the function f (x)= | x - 4|+ | x - 5 | where f (x) represents the height of the bank

At x = 4 . 5 the value of the functions f (x) is

Options

A. 1
B. `-1`
C. 0
D. 10

Answer

To find the value of the function \( f(x) = |x - 4| + |x - 5| \) at \( x = 4.5 \), we will follow these steps:

### Step 1: Substitute \( x = 4.5 \) into the function
We start by substituting \( x = 4.5 \) into the function \( f(x) \).

\[ f(4.5) = |4.5 - 4| + |4.5 - 5| \]

### Step 2: Calculate each absolute value
Now we will calculate each absolute value separately.

1. Calculate \( |4.5 - 4| \):
\[ |4.5 - 4| = |0.5| = 0.5 \]

2. Calculate \( |4.5 - 5| \):
\[ |4.5 - 5| = |-0.5| = 0.5 \]

### Step 3: Add the results
Now, we add the results from the absolute values calculated in Step 2.

\[ f(4.5) = 0.5 + 0.5 = 1 \]

### Final Answer
Thus, the value of the function \( f(x) \) at \( x = 4.5 \) is:

\[ \boxed{1} \]

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