Question:
Let $f(x)=x, g(x)=\frac{1}{x}$ and $h(x)=f(x) g(x)$. Then, $h(x)=1$
(a) x ∈ R
(b) x ∈ Q
(c) x ∈ R − Q
(d) x ∈ R, x ≠ 0
Solution:
(d) x ∈ R, x ≠ 0
Given:
$f(x)=x, g(x)=\frac{1}{x}$ and $h(x)=f(x) g(x)$
Now,
$h(x)=x \times \frac{1}{x}=1$
We observe that the domain of $f$ is $\mathbb{R}$ and the domain of $g$ is $\mathbb{R}-\{0\}$.
$\therefore$ Domain of $h=$ Domain of $f \cap$ Domain of $g=\mathbb{R} \cap[\mathbb{R}-\{0\}]=\mathbb{R}-\{0\}$
$\Rightarrow x \in \mathrm{R}, x \neq 0$
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