If gx-x2-x-1 and gofx-4x2-10x-5- then the value of 2f54 -4 is equal to

Given, g(x)=x^2+x 1 gof(x)=4x^2 10x+5 ⇒ g[ f((x)]=4x^2 10x+5 Put x=54 g[ f( 54)]=4(54 )^2 10( 54)+5 ⇒ f^2(54 )+f(54 ) 1=254 504+5= 54 ⇒ f^2(54 )+f(54 )+14=0 ⇒( ...

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Byju's Answer

Standard XII

Chemistry

Auto Protolysis of Water

If gx=x2+x-1 ...

Question

If $g (x) = x^{2} + x - 1$ and $g o f (x) = 4 x^{2} - 10 x + 5,$ then the value of $2 f (\frac{5}{4}) + 4$ is equal to

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Solution

The correct option is C $3$
Given, $g (x) = x^{2} + x - 1$
$g o f (x) = 4 x^{2} - 10 x + 5$
$\Rightarrow g [f ((x)] = 4 x^{2} - 10 x + 5$
Put $x = \frac{5}{4}$
$g [f (\frac{5}{4})] = 4 {(\frac{5}{4})}^{2} - 10 (\frac{5}{4}) + 5$
$\Rightarrow f^{2} (\frac{5}{4}) + f (\frac{5}{4}) - 1 = \frac{25}{4} - \frac{50}{4} + 5 = - \frac{5}{4}$
$\Rightarrow f^{2} (\frac{5}{4}) + f (\frac{5}{4}) + \frac{1}{4} = 0$
$\Rightarrow {(f (\frac{5}{4}) + \frac{1}{2})}^{2} = 0$
$\Rightarrow f (\frac{5}{4}) = - \frac{1}{2}$
$\Rightarrow 2 f (\frac{5}{4}) + 4 = 3$

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If g(x)=x2+x−1 and gof(x)=4x2−10x+5, then the value of 2f(54)+4 is equal to

The correct option is C 3Given, g(x)=x2+x−1 gof(x)=4x2−10x+5 ⇒g[f((x)]=4x2−10x+5 Put x=54 g[f(54)]=4(54)2−10(54)+5 ⇒f2(54)+f(54)−1=254−504+5=−54 ⇒f2(54)+f(54)+14=0 ⇒(f(54)+12)2=0 ⇒f(54)=−12 ⇒2f(54)+4=3

If $g (x) = x^{2} + x - 1$ and $g o f (x) = 4 x^{2} - 10 x + 5,$ then the value of $2 f (\frac{5}{4}) + 4$ is equal to