If f:R R be defined by f(x) = 3 x 2 - 5 and g:R R by g(x) = x 2 + 1 . Then, gof is

It is given that,, f(x) = 3 x 2 - 5 and g(x) = x 2 + 1 gof = g f(x) = g ( 3 x 2 - 5 ) = - 5 ( 3 x 2 - 5 ) 2 + 1 = - 5 9 x 4 - 30 x 2 + 25 + 1 = - 5 9 x 4 - 30 x 2 + 26

Relations and Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp.Q.38,Page 15

Question

If $f:R \to R$ be defined by $f(x) = 3{x^2} - 5$ and $g:R \to R$ by $g(x) = \frac{x}{{{x^2} + 1}}$.

Then, gof is

(a) $\frac{{3{x^2} - 5}}{{9{x^4} - 30{x^2} + 26}}$ ✓ Correct
(b) $\frac{{3{x^2} - 5}}{{9{x^4} - 6{x^2} + 26}}$
(c) $\frac{{3{x^2}}}{{{x^4} + 2{x^2} - 4}}$
(d) $\frac{{3{x^2}}}{{9{x^4} + 30{x^2} - 2}}$

Step-by-step Solution

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

$gof = g\{ f(x)\} = g\left( {3{x^2} - 5} \right)$
$= \frac{{3{x^2} - 5}}{{{{\left( {3{x^2} - 5} \right)}^2} + 1}} = \frac{{3{x^2} - 5}}{{9{x^4} - 30{x^2} + 25 + 1}}$

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

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