Let f x - x 2-1- Then- which of the following is correct-A- fx y-fx fyB- fx y - fx fyC- fx y - fx fyD- None of these

The correct option is C f(xy) ≤ f(x) f(y) We have, f(x) = √(x^2+1) f(xy) = √(1+x^2y^2) f(x).f(y) = √(1+x^2)√(1+y^2) =√((1+x^2)(1+y^2)) =√(1+x^2+y^2+x^2y^2) ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

Let f x =√ x ...

Question

Let $f (x) = \sqrt{x^{2} + 1}$ . Then, which of the following is correct?

$f (x y) = f (x) f (y)$

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$f (x y) \geq f (x) f (y)$

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$f (x y) \leq f (x) f (y)$

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None of these

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Solution

The correct option is C
$f (x y) \leq f (x) f (y)$

We have, $f (x) = \sqrt{x^{2} + 1} f (x y) = \sqrt{1 + x^{2} y^{2}} f (x) . f (y) = \sqrt{1 + x^{2}} \sqrt{1 + y^{2}} = \sqrt{(1 + x^{2}) (1 + y^{2})} = \sqrt{1 + x^{2} + y^{2} + x^{2} y^{2}} ∵ f (x y) \leq f (x) . f (y)$

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Similar questions

Q. Let

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

. Then, which of the following is correct?

(a)

f (x y) = f (x) f (y)

(b)

f (x y) \geq f (x) f (y)

(c)

f (x y) \leq f (x) f (y)

(d) none of these

$If f (x) = \sqrt{1 + x^{2}}, then$ ____

Q. Let for all

x > 0, f (x) = lim n \to \infty n (x^{1 / n} - 1)

, then

Q. If f(x) = cos (log x), then the value of f(x) f(y) −

\frac{1}{2} \{f (\frac{x}{y}) + f (x y)\}

is
(a) −1
(b) 1/2
(c) −2
(d) None of these

If $f (x) = c o s (l o g x)$ , then $f (x) f (y) - \frac{1}{2} {f (\frac{x}{y}) + f (x y)}$ has the value

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Let f(x)=√x2+1. Then, which of the following is correct?

The correct option is C f(xy)≤f(x) f(y) We have, f(x)=√x2+1f(xy)=√1+x2y2f(x).f(y)=√1+x2√1+y2=√(1+x2)(1+y2)=√1+x2+y2+x2y2∵f(xy)≤f(x).f(y)

Let $f (x) = \sqrt{x^{2} + 1}$ . Then, which of the following is correct?

The correct option is C
$f (x y) \leq f (x) f (y)$

We have, $f (x) = \sqrt{x^{2} + 1} f (x y) = \sqrt{1 + x^{2} y^{2}} f (x) . f (y) = \sqrt{1 + x^{2}} \sqrt{1 + y^{2}} = \sqrt{(1 + x^{2}) (1 + y^{2})} = \sqrt{1 + x^{2} + y^{2} + x^{2} y^{2}} ∵ f (x y) \leq f (x) . f (y)$