Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

\mathrm{f \: and \: \: g} are two differentiable function which satisfy the condition \mathrm{g^{\prime}(a)=2, g(a)=b} and \mathrm{(f \circ g)=I} (identity function), then\mathrm{ f^{\prime}(b)} is equal to
 

Option: 1

\frac{2}{3}


Option: 2

\frac{1}{2}


Option: 3

2


Option: 4

\text{none of these}


Answers (1)

best_answer

\mathrm{(f \circ g) x=I(x)=x \: or \: f[g(x)]=x}

Differentiating both sides \mathrm{ f^{\prime}[g(x)] g^{\prime}(x)=1}

Put \mathrm{ x=a, f^{\prime}[g(a)] g^{\prime}(a)=1}

Now, put \mathrm{ g(a)=b\: and \: g^{\prime}(a)=2}

\mathrm{ f^{\prime}[b] \cdot 2=1 \Rightarrow f^{\prime}(b)=\frac{1}{2} }

Hence option 2 is correct.

Posted by

HARSH KANKARIA

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 application soon at jeemain.nta.nic.in; BTech exam dates
anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications open soon at jeemain.nta.nic.in; exam dates out
anam-khan

JEE Main 2026: Top NITs still competitive for PwD candidates, show BTech CSE closing ranks

Latest Question