Let `f:Nrarr R,f(x)=2x-1`
`g:z rarrR,g(x)=(x^(2))/(2)`, then `(gof)(0)` is :

Options

A. `-(1)/(2)`
B. `(1)/(2)`
C. 1
D. none of these

Answer

To solve the problem, we need to find the value of \( (g \circ f)(0) \), which means we will first evaluate \( f(0) \) and then use that result to evaluate \( g(f(0)) \).

### Step 1: Evaluate \( f(0) \)
The function \( f \) is defined as:
\[ f(x) = 2x - 1 \]
Now, we substitute \( x = 0 \):
\[ f(0) = 2(0) - 1 = 0 - 1 = -1 \]

### Step 2: Evaluate \( g(f(0)) \)
Now we need to find \( g(f(0)) \), which is \( g(-1) \). The function \( g \) is defined as:
\[ g(x) = \frac{x^2}{2} \]
Substituting \( x = -1 \):
\[ g(-1) = \frac{(-1)^2}{2} = \frac{1}{2} \]

### Final Answer
Thus, the value of \( (g \circ f)(0) \) is:
\[ \frac{1}{2} \]