Let `f(x)=x^(2) and g(x)=sqrtx`, then :

Options

A. `gof(3)=9`
B. `gof(-3)=9`
C. `gof(3)=3`
D. `gof(-9)=3`

Answer

To solve the problem, we need to find the value of \( g(f(x)) \) where \( f(x) = x^2 \) and \( g(x) = \sqrt{x} \).

### Step-by-Step Solution:

1. **Identify the Functions**:
- We have \( f(x) = x^2 \) and \( g(x) = \sqrt{x} \).

2. **Find \( g(f(x)) \)**:
- To find \( g(f(x)) \), we need to substitute \( f(x) \) into \( g(x) \).
- This means we will replace \( x \) in \( g(x) \) with \( f(x) \):
\[ g(f(x)) = g(x^2) \]

3. **Substitute \( f(x) \) into \( g(x) \)**:
- Now, substitute \( x^2 \) into \( g(x) \):
\[ g(x^2) = \sqrt{x^2} \]

4. **Simplify \( g(x^2) \)**:
- The square root of \( x^2 \) is \( |x| \) (the absolute value of \( x \)):
\[ g(x^2) = |x| \]

5. **Evaluate \( g(f(x)) \) for specific values**:
- Now, we can evaluate \( g(f(x)) \) for specific values of \( x \):
- For \( x = 3 \):
\[ g(f(3)) = g(3^2) = g(9) = \sqrt{9} = 3 \]
- For \( x = -3 \):
\[ g(f(-3)) = g((-3)^2) = g(9) = \sqrt{9} = 3 \]
- For \( x = -9 \):
\[ g(f(-9)) = g((-9)^2) = g(81) = \sqrt{81} = 9 \]

6. **Conclusion**:
- The values we calculated are:
- \( g(f(3)) = 3 \)
- \( g(f(-3)) = 3 \)
- \( g(f(-9)) = 9 \)

### Final Answer:
- The correct answer from the options provided is \( g(f(3)) = 3 \).