Consider the following statements:<br>1. The relation f defined by f(x)=\begin{cases}x^{3},&0\leq x\leq2\\ 4x,&2\leq x\leq8\end{cases} is a function.<br>2. The relation g defined by g(x)=\begin{cases}x^{2},&0\leq x\leq4\\ 3x,&4\leq x\leq8\end{cases} is a function.<br>Which of the statements given above is/are correct?
- A. 1 <strong>ONLY</strong> ✓
- B. 2 <strong>ONLY</strong>
- C. <strong>BOTH</strong> 1 and 2
- D. Neither 1 nor 2
Correct Answer: A. 1 <strong>ONLY</strong>
Explanation
For f(x), check the split point x=2: 2^3 = 8 and 4(2) = 8. It yields a unique value, so f(x) is a function. For g(x), check the split point x=4: 4^2 = 16 but 3(4) = 12. Since 16 \neq 12, g(x) assigns two values to x=4, so it is not a function.
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