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 step by step, we need to evaluate the functions \( f(x) \) and \( g(x) \) given in the question.

### Step 1: Define the Functions
We are given two functions:
- \( f(x) = x^2 \)
- \( g(x) = \sqrt{x} \)

### Step 2: Evaluate \( g(f(x)) \)
We need to find \( g(f(x)) \). This means we will substitute \( f(x) \) into \( g(x) \).

\[ g(f(x)) = g(x^2) \]

### Step 3: Substitute \( f(x) \) into \( g(x) \)
Now, we will substitute \( x^2 \) into \( g(x) \):

\[ g(x^2) = \sqrt{x^2} \]

### Step 4: Simplify \( g(x^2) \)
The square root of \( x^2 \) is:

\[ g(x^2) = |x| \]

This means that \( g(f(x)) = |x| \).

### Step 5: Evaluate Specific Values
Now, we can evaluate \( g(f(x)) \) for specific values of \( x \):

1. For \( x = 3 \):
\[ g(f(3)) = g(3^2) = g(9) = \sqrt{9} = 3 \]

2. For \( x = -3 \):
\[ g(f(-3)) = g((-3)^2) = g(9) = \sqrt{9} = 3 \]

3. For \( x = -9 \):
\[ g(f(-9)) = g((-9)^2) = g(81) = \sqrt{81} = 9 \]

### Step 6: Conclusion
From our evaluations:
- \( g(f(3)) = 3 \)
- \( g(f(-3)) = 3 \)
- \( g(f(-9)) = 9 \)

Thus, the correct options based on the evaluations are:
- \( g(3) = 3 \)
- \( g(-3) = 3 \)
- \( g(-9) = 9 \)