Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let  \mathrm{S=\{1,2,3,4,5,6,7,8,9,10\}}. Define \mathrm{f: S \rightarrow S} as  \mathrm{f(n)=\left\{\begin{array}{cc} 2 n, & \text { if } n=1,2,3,4,5 \\ 2 n-11, & \text { if } n=6,7,8,9,10 \end{array}\right.}

Let  \mathrm{g: S \rightarrow S}  be a function such that  \mathrm{f \circ g(n)=\left\{\begin{array}{ll} n+1 & , \text { if } n \text { is odd } \\ n-1, & \text { if } n \text { is even } \end{array},\right.} Then  \mathrm{g(10)(g(1)+g(2)+g(3)+g(4)+g(5))} is equal to ___________.

Option: 1

190


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{f(g(n))= \begin{cases}2 g(n), & \text { if } g(n)=1,2,3,4,5 \\ 2 g(n)-11, & i f(g(n)=6,7,8,9,10\end{cases}}

\mathrm{f(1)=2, f(2)=4, f(3)=6, f(4)=8, f(5)=10 }\\

\mathrm{f(6)=1, f(7)=3, f(8)=5, f(9)=7, f(10)=9}

\mathrm{f(g(n))=\left\{\begin{array}{lll} n+1, & \text { if } & n=1,3,5,7,9 \\ n-1, & \text { if } & n=2,4,0,8,10 \end{array}\right.}

\mathrm{\Rightarrow f(g(1))=2, fo g(3)=4, f og(5)=6, f og(7)=8, f o g(9)=10} \\

\mathrm{\Rightarrow f o g(2)=1, fog(4)=3, f og(6)=5, f og(8)=7, f og(10)=9 }

\mathrm{\Rightarrow g(1)=f^{-1}(2)=1, \quad g(2)=f^{-1}(1)=6, \quad g(3)=f-1(4)=2}, \\

\mathrm{g(4)=f^{-1}(3)=7, \quad g(5)=f^{-1}(6)=3, g(10)=f^{-1}(g)=10 } \\

\mathrm{g(10)(g(1)+g(2)+g(3)+g(4)+g(5))=10(1+6+2+7+3)=190}

Hence answer is \mathrm{190}

 

Posted by

vinayak

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

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads
anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26
anam-khan

JEE Main City Intimation Slip 2025 Live: NTA session 2 exam city slips soon at jeemain.nta.nic.in

Latest Question