Let f x - x - g x -1- x and h x - f x g x - Then- h x -1 forA- x - QB- x - QC- x - R - x - QD- x - R - Q

The correct option is C x ϵ R, x ≠ Q Given: f(x) = x, g(x) = 1/x and h(x) = f(x) g(x) Now, h(x) = x ×1/x=1 We observe that the domain of f is R and the domain ...

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Byju's Answer

Standard XII

Mathematics

Domain

Let f x = x ,...

Question

Let $f (x) = x, g (x) = \frac{1}{x}$ and $h (x) = f (x) g (x)$ . Then, $h (x) = 1$ for

$x ϵ Q$

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$x ϵ Q$

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$x ϵ R - Q$

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$x ϵ R, x \neq Q$

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Solution

The correct option is D
$x ϵ R, x \neq Q$

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 R and the domain of g is R - {0}
$∴$ Domain of h = Domain of $f \cap$ Domain of g $= R \cap [R - {0}] = R - {0} \Rightarrow x ϵ R, x \neq 0$

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Similar questions

Q. 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

Q. Let

f (x) = x^{2} - \frac{1}{x^{2}}

and

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f (x) = x^{2} + \frac{1}{x^{2}}

and

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Q. Let

f (x) = [\frac{x}{[x]}], g (x) = [x [\frac{1}{x}]]

and

h (x) = [\frac{[x]}{x}],

, then

lim x \to 2^{-} f (x) + lim x \to {\frac{1}{2}}^{+} g (x) + lim x \to 2^{+} h (x) =

Q. Let f(x), g(x), h(x) be continous in [0, 2a] and satisfies

f (2 a - x) = f (x), g (2 a - x) = g (x), h (x) + h (2 a - x) = 3, f (2 a - x) g (2 a - x) = f (x) g (x) t h e n \int_{0}^{2 a} f (x) g (x) h (x) d x =

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Let f(x)=x,g(x)=1x and h(x)=f(x) g(x). Then, h(x)=1 for

The correct option is D xϵR, x≠Q Given: f(x)=x,g(x)=1x and h(x)=f(x) g(x) Now, h(x)=x×1x=1 We observe that the domain of f is R and the domain of g is R - {0} ∴ Domain of h = Domain of f∩ Domain of g =R∩[R−{0}]=R−{0}⇒xϵR,x≠0

Let $f (x) = x, g (x) = \frac{1}{x}$ and $h (x) = f (x) g (x)$ . Then, $h (x) = 1$ for