Let f- - - be defined bynfx-3x2-5 and g- - - gx-xx2-1- Then gof is -

Given : nbsp;f(x)=3x^2 5,f:ℝ → ℝ nbsp; nbsp; and g(x)=xx^2+1,g:ℝ → ℝ Here, nbsp; f(x)=3x^2 5, and g(x)=xx^2+1 nbsp; nbsp; ∴ gof=g(f(x))=f(x)(f(x) ...

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Standard X

Mathematics

Nature of Roots

Let f:ℝ → ℝ b...

Question

Let $f : R \to R$ be defined byn

$f (x) = 3 x^{2} - 5 and g : R \to R$

$g (x) = \frac{x}{x^{2} + 1} .$ Then $g o f$ is ?

\frac{3 x^{2} - 5}{9 x^{4} - 30 x^{2} + 26}

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\frac{3 x^{2} - 5}{9 x^{4} - 6 x^{2} + 26}

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\frac{3 x^{2}}{9 x^{4} + 30 x^{2} - 2}

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\frac{3 x^{2}}{x^{4} + 2 x^{2} - 4}

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Solution

The correct option is A $\frac{3 x^{2} - 5}{9 x^{4} - 30 x^{2} + 26}$
Given : $f (x) = 3 x^{2} - 5, f : R \to R$

and $g (x) = \frac{x}{x^{2} + 1}, g : R \to R$

Here, $f (x) = 3 x^{2} - 5, and g (x) = \frac{x}{x^{2} + 1}$

$∴ g o f = g (f (x)) = \frac{f (x)}{(f (x))^{2} + 1}$

$= \frac{3 x^{2} - 5}{(3 x^{2} - 5)^{2} + 1}$

$∴ g o f = \frac{3 x^{2} - 5}{9 x^{4} - 30 x^{2} + 26}$

Hence, the correct answer is option (a).

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Nature of Roots

Standard X Mathematics

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Let f:R → R be defined byn f(x)=3x2−5 and g:R → R g(x)=xx2+1. Then gof is ?

The correct option is A 3x2−59x4−30x2+26Given : f(x)=3x2−5,f:R → R and g(x)=xx2+1,g:R → R Here, f(x)=3x2−5, and g(x)=xx2+1 ∴ gof=g(f(x))=f(x)(f(x))2+1 =3x2−5(3x2−5)2+1 ∴ gof=3x2−59x4−30x2+26 Hence, the correct answer is option (a).

Let $f : R \to R$ be defined byn

$f (x) = 3 x^{2} - 5 and g : R \to R$

$g (x) = \frac{x}{x^{2} + 1} .$ Then $g o f$ is ?