Let ` f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ` ,where [.] is the greatest integer function . Then h(-1) is

Options

A. 0
B. `- oo`
C. 3
D. None of these

Answer

To solve the problem step by step, we need to evaluate \( h(-1) \) where \( h(x) = f(g(x)) \), \( f(x) = [x] \) (the greatest integer function), and \( g(x) = |x| \) (the absolute value function).

### Step 1: Find \( g(-1) \)
We start by calculating \( g(-1) \):
\[ g(x) = |x| \implies g(-1) = |-1| = 1 \]

**Hint:** Remember that the absolute value of a negative number is its positive counterpart.

### Step 2: Substitute \( g(-1) \) into \( h(x) \)
Now we substitute \( g(-1) \) into the function \( h(x) \):
\[ h(-1) = f(g(-1)) = f(1) \]

**Hint:** We are now looking for the value of the function \( f \) at the point we just calculated.

### Step 3: Find \( f(1) \)
Next, we need to evaluate \( f(1) \):
\[ f(x) = [x] \implies f(1) = [1] \]
The greatest integer less than or equal to 1 is 1.

**Hint:** The greatest integer function returns the largest integer that is less than or equal to the given number.

### Step 4: Conclusion
Putting it all together, we find:
\[ h(-1) = f(1) = 1 \]

Thus, the final answer is:
\[ \boxed{1} \]