Question

Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\]  and h(x) = f(x) g(x). Then, h(x) = 1

Options

• (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,

\[h(x) = x \times \frac{1}{x} = 1\] We observe that the domain of f is \[\mathbb{R}\] and the domain of g is  \[\mathbb{R} - \left\{ 0 \right\}\] ∴ Domain of h = Domain of f ⋂ Domain of g = \[\mathbb{R} \cap \left[ \mathbb{R} - \left\{ 0 \right\} \right] = \mathbb{R} - \left\{ 0 \right\}\]

\[\Rightarrow\] x ∈ R, x ≠ 0