# Let f(x) = x,

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 $g=\mathbb{R} \cap[\mathbb{R}-\{0\}]=\mathbb{R}-\{0\}$

$\Rightarrow x \in \mathrm{R}, x \neq 0$