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) ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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).

Suggest Corrections

Similar questions

Q. Find

g o f

and

f o g,

f : R \to R

and

g : R \to R

are given by

f (x) = cos x

and

g (x) = 3 x^{2}

. Show that

g o f \neq f o g

Q. Let

f : R \to R

be defined as

f (x) = 2 x - 1

and

g : R - {1} \to R

be defined as

g (x) = \frac{x - \frac{1}{2}}{x - 1}

. Then the composition function

f (g (x))

is:

Q. Let the functions

f : R \to R

and

g : R \to R

be defined as:

f (x) = {\begin{matrix} x + 2, & x < 0 x^{2}, & x \geq 0 \end{matrix} and g (x) = {\begin{matrix} x^{3}, & x < 1 3 x - 2, & x \geq 1 \end{matrix}

Then, the number of points in

R

where

(f o g) (x)

is non differentiable is equal to :

Q. Let

f : R \to R, g : R \to R

and

h : R \to R

be differentiable functions such that

f (x) = x^{3} + 3 x + 2, g (f (x)) = x

and

h (g (g (x))) = x

for all

x \in R

. Then

Q. Let

f, g : R \to R

be defined by

f (x) = x^{2} - \frac{cos x}{2}

and

g (x) = \frac{x sin x}{2}

. Then

Join BYJU'S Learning Program

Explore more

Nature of Roots

Standard X Mathematics

Join BYJU'S Learning Program

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 ?