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Let F(X) = X, G ( X ) = 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 - Mathematics

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Question

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

Options

  • (a) x ∈ R

  • (b) x ∈ Q

  • (c) x ∈ R − Q

  • (d) x ∈ R, x ≠ 0

     
MCQ

Solution

(d) x ∈ R, x ≠ 0

Given:
f(x) = x,  \[g\left( x \right) = \frac{1}{x}\]  and h(x) = f(xg(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
 
 
 
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Chapter 3: Functions - Exercise 3.6 [Page 44]

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RD Sharma Mathematics [English] Class 11
Chapter 3 Functions
Exercise 3.6 | Q 19 | Page 44

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