Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Mcq Single Correct #72
The function \(f:\mathbb R\to\mathbb R\) defined by \(f(x)=2^x+2^{|x|}\) is
✅ Step-by-Step Solution
Final Answer: Option (D): Many-one and into
- For \(x<0\), write \(t=2^x\in(0,1)\). Then \(f(x)=t+t^{-1}\) decreases towards 2 as \(x\to0^-\). For \(x\ge0\), \(f(x)=2^{x+1}\) increases from 2. Its range is \([2,\infty)\), and \(f(-1)=5/2=f(\log_2(5/4))\), so it is many-one and into.
Master Chapter 1: Relations And Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Relations And Functions.
← Previous Question
Let \(A,B\) be finite sets with \(m,n\) elements. The number of…
Next Question →If \(|A|=5\) and \(|B|=6\), the number of one-one and onto mappings…
More Practice Questions in Relations And Functions
Related Questions in Relations And Functions
Class 12 Relations And Functions · Mcq Single Correct
Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the minimum number of…
Class 12 Relations And Functions · Mcq Single Correct
The function \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=e^x\) is
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to\mathbb{R}\)…
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to S\), defined by \(f(x)=\sin x-\sqrt{3}\cos x+1\), is onto, then the…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A=\{1,2,3\}\) and \(B=\{a,b,c\}\). Then the number of bijective functions from \(A\) to…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A\) and \(B\) be two finite sets having \(m\) and \(n\) elements respectively. Then the…