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

Options

A. `1/2`
B. 44198
C. 1
D. none of these

Answer

To solve the problem step by step, we need to find \( (g \circ f)(0) \), which means we will first evaluate \( f(0) \) and then substitute that result into \( g(x) \).

### Step 1: Evaluate \( f(0) \)
The function \( f \) is given by:
\[ f(x) = 2x - 1 \]
Now, substituting \( x = 0 \):
\[ f(0) = 2(0) - 1 = -1 \]

### Step 2: Substitute \( f(0) \) into \( g(x) \)
Next, we need to evaluate \( g(f(0)) = g(-1) \). The function \( g \) is given by:
\[ g(x) = \frac{x^2}{2} \]
Now substituting \( x = -1 \):
\[ g(-1) = \frac{(-1)^2}{2} = \frac{1}{2} \]

### Conclusion
Thus, \( (g \circ f)(0) = g(f(0)) = g(-1) = \frac{1}{2} \).

### Final Answer
\[ (g \circ f)(0) = \frac{1}{2} \]

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