Find \( h(x) \)
Question:
Let
\[ f(x)=x,\qquad g(x)=\frac1x \]
and
\[ h(x)=f(x)g(x) \]
Then,
\[ h(x)=1 \]
for
(a) \(x\in R\)
(b) \(x\in Q\)
(c) \(x\in R-Q\)
(d) \(x\in R,\; x\ne0\)
Solution:
\[ h(x)=f(x)g(x) \]
\[ =x\cdot\frac1x \]
\[ =1 \]
This is defined only when
\[ x\ne0 \]
Therefore,
\[ h(x)=1 \quad \text{for} \quad x\in R,\; x\ne0 \]
\[ \boxed{\text{Correct Answer: (d)}} \]