Given two functions such that fx- 0 and gx - 0 for all real x- the correct inequality is-I- fx - gx - 0II- fx gx - 0III- fxgx - 0

The correct option is E I and III f(x)≥ 0 and g(x)≥ 0 , which says that both f and g are non negativeSum of non negative functions will b ...

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Standard XII

Mathematics

Combination

Given two fun...

Question

Given two functions such that $f (x) \geq 0$ and $g (x) \geq 0$ for all real $x$ , the correct inequality is:
I. $f (x) + g (x) \geq 0$
II. $f (x) g (x) > 0$
III. $f (x) g (x) \geq 0$

I only

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II only

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III only

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I and II

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I and III

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Solution

The correct option is E I and III
$f (x) \geq 0$ and $g (x) \geq 0$ , which says that both $f$ and $g$ are non negative
Sum of non negative functions will be non negative . so $f (x) + g (x) \geq 0$
product of two non negative functions will be non negative

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If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that

Q. Let

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x \in (a, b), f^{n} (x) = g (x)

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g (x) = \frac{1}{x}

and h(x) = f(x) g(x). Then, h(x) = 1
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(d) x ∈ R, x ≠ 0

Q. Let

\int \frac{f^{'} (x) g (x) - g^{'} (x) f (x)}{(f (x) + g (x)) \sqrt{f (x) g (x) - g^{2} (x)}} d x = \sqrt{m} {tan}^{- 1} (\sqrt{\frac{f (x) - g (x)}{n g (x)}}) + C

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Given two functions such that f(x)≥0 and g(x)≥0 for all real x, the correct inequality is:I. f(x)+g(x)≥0II. f(x)g(x)>0III. f(x)g(x)≥0

The correct option is E I and IIIf(x)≥0 and g(x)≥0 , which says that both f and g are non negativeSum of non negative functions will be non negative . so f(x)+g(x)≥0product of two non negative functions will be non negative

Given two functions such that $f (x) \geq 0$ and $g (x) \geq 0$ for all real $x$ , the correct inequality is:
I. $f (x) + g (x) \geq 0$
II. $f (x) g (x) > 0$
III. $f (x) g (x) \geq 0$

The correct option is E I and III
$f (x) \geq 0$ and $g (x) \geq 0$ , which says that both $f$ and $g$ are non negative
Sum of non negative functions will be non negative . so $f (x) + g (x) \geq 0$
product of two non negative functions will be non negative