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If f(x)=1/x and g(x) = 0 then fog is...

If `f(x)=1/x and g(x) = 0` then fog is

A

Not defined

B

Defined `AA x inR`

C

Defined `AA x in [0, 1]`

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find \( f(g(x)) \) given the functions \( f(x) = \frac{1}{x} \) and \( g(x) = 0 \). ### Step-by-Step Solution: 1. **Identify the functions**: - We have \( f(x) = \frac{1}{x} \) - We have \( g(x) = 0 \) 2. **Find \( g(x) \)**: - Since \( g(x) = 0 \), this means for any input \( x \), the output of \( g \) is always \( 0 \). 3. **Substitute \( g(x) \) into \( f \)**: - We need to find \( f(g(x)) \). Since \( g(x) = 0 \), we substitute \( 0 \) into \( f \): \[ f(g(x)) = f(0) \] 4. **Evaluate \( f(0) \)**: - Now we calculate \( f(0) \): \[ f(0) = \frac{1}{0} \] - The expression \( \frac{1}{0} \) is undefined in mathematics. 5. **Conclusion**: - Since \( f(0) \) is undefined, we conclude that \( f(g(x)) \) is also undefined. Thus, the final answer is that \( f(g(x)) \) is **not defined**.
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