If f- g and h are three valued function defined by fx -x-1 - gx - 1-x - hx - 2x2 - 3find the value of 2f-g-h at x-3x-2-

Given x=3x 2 ⇒ 2x=2,x=1 therefore f(x),g(x),h(x) at x=1 are f(x)=√(x 1)=√(1 1)=0 at x=1 g(x)=1x=1 at x=1 h(x)=2x ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

If f, g and h...

Question

If f, g and h are three valued function defined by
$f (x) = \sqrt{x - 1}$ , $g (x) = \frac{1}{x}$ , $h (x) = 2 x^{2} + 3$
find the value of $2 f + g + h$ at $x = 3 x - 2$ .

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Solution

given $x = 3 x - 2$

$\Rightarrow 2 x = 2, x = 1$

therefore $f (x), g (x), h (x)$ at $x = 1$ are

$f (x) = \sqrt{x - 1} = \sqrt{1 - 1} = 0$ at $x = 1$

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

$h (x) = 2 x^{2} + 3 = 2 + 3 = 5$ at $x = 1$

therefore $2 f + g + h = 0 + 1 + 5 = 6$

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If f, g and h are three valued function defined byf(x)=√x−1 , g(x)=1x , h(x)=2x2+3find the value of 2f+g+h at x=3x−2.

given x=3x−2⇒2x=2,x=1therefore f(x),g(x),h(x) at x=1 aref(x)=√x−1=√1−1=0 at x=1g(x)=1x=1 at x=1h(x)=2x2+3=2+3=5 at x=1therefore 2f+g+h=0+1+5=6

If f, g and h are three valued function defined by
$f (x) = \sqrt{x - 1}$ , $g (x) = \frac{1}{x}$ , $h (x) = 2 x^{2} + 3$
find the value of $2 f + g + h$ at $x = 3 x - 2$ .

given $x = 3 x - 2$

$\Rightarrow 2 x = 2, x = 1$

therefore $f (x), g (x), h (x)$ at $x = 1$ are

$f (x) = \sqrt{x - 1} = \sqrt{1 - 1} = 0$ at $x = 1$

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

$h (x) = 2 x^{2} + 3 = 2 + 3 = 5$ at $x = 1$

therefore $2 f + g + h = 0 + 1 + 5 = 6$