If f is the greatest integer function defined on R as `f(x)=[x]` and g is the modulus function defined on R as `g(x)=|x|`, then the value of `(gof)(-(5)/(3))` is

Options

A. 1
B. 2
C. 3
D. none of these

Answer

To solve the problem, we need to evaluate the composition of functions \( g(f(x)) \) at \( x = -\frac{5}{3} \).

### Step 1: Evaluate \( f\left(-\frac{5}{3}\right) \)

The function \( f(x) \) is defined as the greatest integer function, denoted as \( f(x) = [x] \). This function returns the greatest integer less than or equal to \( x \).

First, we calculate \( -\frac{5}{3} \):
\[ -\frac{5}{3} \approx -1.6667 \]
Now, we apply the greatest integer function:
\[ f\left(-\frac{5}{3}\right) = \left[-\frac{5}{3}\right] = -2 \]

### Step 2: Evaluate \( g(f(-\frac{5}{3})) \)

Next, we need to apply the modulus function \( g(x) = |x| \) to the result we obtained from step 1.

Now we calculate:
\[ g(f(-\frac{5}{3})) = g(-2) = |-2| = 2 \]

### Final Answer

Thus, the value of \( g(f(-\frac{5}{3})) \) is:
\[ \boxed{2} \]

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