If `f={(1,4),(2,5),(3,6)}` and `g={(4,8),(5,7),(6,9)}`, then gof is

Options

A. `{phi}`
B. `{(1,8),(2,7),(3,9)}`
C. `{(1,7),(2,8),(3,9)}`
D. none of these

Answer

To find the composition of the functions \( g \) and \( f \), denoted as \( g \circ f \), we need to evaluate \( g(f(x)) \) for each element in the domain of \( f \).

### Step-by-Step Solution:

1. **Identify the functions**:
- The function \( f \) is given as \( f = \{(1,4), (2,5), (3,6)\} \).
- The function \( g \) is given as \( g = \{(4,8), (5,7), (6,9)\} \).

2. **Determine the outputs of \( f \)**:
- For \( x = 1 \):
\[ f(1) = 4 \]
- For \( x = 2 \):
\[ f(2) = 5 \]
- For \( x = 3 \):
\[ f(3) = 6 \]

3. **Evaluate \( g(f(x)) \)** for each output of \( f \):
- For \( f(1) = 4 \):
\[ g(f(1)) = g(4) = 8 \]
- For \( f(2) = 5 \):
\[ g(f(2)) = g(5) = 7 \]
- For \( f(3) = 6 \):
\[ g(f(3)) = g(6) = 9 \]

4. **Compile the results**:
- Thus, the composition \( g \circ f \) can be represented as:
\[ g \circ f = \{(1,8), (2,7), (3,9)\} \]

### Final Result:
The composition \( g \circ f \) is:
\[ g \circ f = \{(1,8), (2,7), (3,9)\} \]