If A={1,2} and B={3,6} and two functions `f: A to B` and `g: A to B` are defined respectively as :
`f(x) =x^(2) + 2 and g(x) =3x`
Find whether `f=g`

Answer

To determine whether the functions \( f \) and \( g \) are equal, we need to evaluate both functions for all elements in the set \( A \) and compare the results.

Given:
- Set \( A = \{1, 2\} \)
- Set \( B = \{3, 6\} \)
- Function \( f(x) = x^2 + 2 \)
- Function \( g(x) = 3x \)

### Step 1: Evaluate \( f(1) \)
To find \( f(1) \):
\[ f(1) = 1^2 + 2 = 1 + 2 = 3 \]

### Step 2: Evaluate \( f(2) \)
To find \( f(2) \):
\[ f(2) = 2^2 + 2 = 4 + 2 = 6 \]

### Step 3: Evaluate \( g(1) \)
To find \( g(1) \):
\[ g(1) = 3 \times 1 = 3 \]

### Step 4: Evaluate \( g(2) \)
To find \( g(2) \):
\[ g(2) = 3 \times 2 = 6 \]

### Step 5: Compare the results
Now we compare the results of \( f \) and \( g \):
- \( f(1) = 3 \) and \( g(1) = 3 \)
- \( f(2) = 6 \) and \( g(2) = 6 \)

Since \( f(x) = g(x) \) for all \( x \) in \( A \), we conclude that:
\[ f = g \]

### Final Conclusion
The functions \( f \) and \( g \) are equal.

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