Let a function fx satisfies f2x-f2y-4x-y and f0- 2 f x - 0 whose domain is - a - and it is differentiable on a - The value of f3 is

The correct option is A 4 f^2(x) f^2(y)=4(x y) #160;and f(0)= 2 ( f ( x )≥ 0 ) f^2(x) f^2(y)=4(x y) #160;Put y=0, f^2(x) f^2(0) ...

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Standard XII

Mathematics

Definition of Functions

Let a functio...

Question

Let a function $f (x)$ satisfies $f^{2} (x) - f^{2} (y) = 4 (x - y)$ and $f (0) = 2 (f (x) \geq 0)$ whose domain is $[a, \infty)$ and it is differentiable on $(a, \infty)$
The value of $f (3)$ is

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Solution

The correct option is A $4$
$f^{2} (x) - f^{2} (y) = 4 (x - y)$

and $f (0) = 2 (f (x) \geq 0)$

$f^{2} (x) - f^{2} (y) = 4 (x - y)$

Put y=0,

$f^{2} (x) - f^{2} (0) = 4 x$

$f^{2} (x) = 4 x + 4$
$f^{2} (3) = 16$

$f (x) = \pm 4$

But given $f (x) \geq 0$ ,

Hence $f (3) = 4$

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Let a function f(x) satisfies f2(x)−f2(y)=4(x−y) and f(0)=2(f(x)≥0)whose domain is [a,∞) and it is differentiable on (a,∞)The value of f(3) is

The correct option is A 4f2(x)−f2(y)=4(x−y) and f(0)=2(f(x)≥0)f2(x)−f2(y)=4(x−y) Put y=0,f2(x)−f2(0)=4x f2(x)=4x+4 f2(3)=16 f(x)=±4But given f(x)≥0, Hencef(3)=4

Let a function $f (x)$ satisfies $f^{2} (x) - f^{2} (y) = 4 (x - y)$ and $f (0) = 2 (f (x) \geq 0)$ whose domain is $[a, \infty)$ and it is differentiable on $(a, \infty)$
The value of $f (3)$ is

The correct option is A $4$
$f^{2} (x) - f^{2} (y) = 4 (x - y)$

and $f (0) = 2 (f (x) \geq 0)$

$f^{2} (x) - f^{2} (y) = 4 (x - y)$

Put y=0,

$f^{2} (x) - f^{2} (0) = 4 x$

$f^{2} (x) = 4 x + 4$
$f^{2} (3) = 16$

$f (x) = \pm 4$

But given $f (x) \geq 0$ ,

Hence $f (3) = 4$