Question

Let f(x) = x, $g\left(x\right)=\frac{1}{x}$ 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

Answer 1

(d) x ∈ R, x ≠ 0

Given:
f(x) = x, $g\left(x\right)=\frac{1}{x}$ and h(x) = f(x) g(x)
Now,
$h\left(x\right)=x\times \frac{1}{x}=1$
We observe that the domain of f is $\mathrm{ℝ}$ and the domain of g is $\mathrm{ℝ}-\left\{0\right\}$.
∴ Domain of h = Domain of f ⋂ Domain of g = $\mathrm{ℝ}\cap \left[\mathrm{ℝ}-\left\{0\right\}\right]=\mathrm{ℝ}-\left\{0\right\}$
$\Rightarrow$x ∈ R, x ≠ 0