Register

ISRO-DEC2017-5

• recategorized by
3,191 views
4 votes
4 votes

Let $f(x)=\log|x|$ and $g(x) =\sin x$. If $A$ is the range of $f(g(x))$ and $B$ is the range of $g(f(x))$ then $A\cap B$ is

  1. $[-1,0]$
  2. $[-1,0)$
  3. $[-\infty ,0]$
  4. $[-\infty ,1]$
• recategorized by
User Avatar

2 Answers

Best answer
10 votes
10 votes

f(g(x)) = log|g(x)| =log |sin x|

  0\leq |sin x| \leq1

which is given to input for log function

and we know in domain of [0,1] log will give range (- \infty ,0]

so here range of f(g(x)) = (- \infty ,0]

g(f(x)) = sin(f(x))  = sin(log|x|)

log|x| will gives values in between - \infty to + \infty

and which is given the input for sin function

-1\leq sinx \leq 1

so range of g(f(x)) is [-1,1]

common of both is [-1,0]

• selected by
User Avatar
1 votes
1 votes
I think it should be A as the log|sinx| { |sinx| vary from 1 to 0 } so range of log|sinx| is -inf to 0
for sin(log|x|) we have log|x| range over Real number so sin(x) range over -1 to 1 and hence intersection is
[-1,0]
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

12 votes
12 votes
2 answers
1
gatecse asked Dec 17, 2017
4,427 views
ISRO-DEC2017-2
Consider the set of integers $I.$ Let $D$ denote "divides with an integer quotient" (e.g. $4D8$ but not $4D7$). Then $D$ is Reflexive, Not Symmetric, Transitive Not Reflexive, Not Anti-symmetric, Transitive Reflexive, Anti-symmetric, Transitive Not Reflexive, Not Anti-symmetric, Not Transitive
Consider the set of integers $I.$ Let $D$ denote "divides with an integer quotient" (e.g. $4D8$ but not $4D7$). Then $D$ isReflexive, Not Symmetric, TransitiveNot Reflexi...
User Avatar
6 votes
6 votes
2 answers
2
gatecse asked Dec 17, 2017
2,727 views
ISRO-DEC2017-9
The function $f:[0,3]\rightarrow [1,29]$ defined by $f(x)=2x^{3}-15x^{2}+36x+1$ is injective and surjective surjective but not injective injective but not surjective neither injective nor surjective
The function $f:[0,3]\rightarrow [1,29]$ defined by $f(x)=2x^{3}-15x^{2}+36x+1$ isinjective and surjectivesurjective but not injectiveinjective but not surjectiveneither ...
User Avatar
3 votes
3 votes
3 answers
3
gatecse asked Dec 17, 2017
4,574 views
ISRO-DEC2017-8
The number of elements in the power set of $\{\{1,2\},\{2,1,1\},\{2,1,1,2\}\}$ is $3$ $8$ $4$ $2$
The number of elements in the power set of $\{\{1,2\},\{2,1,1\},\{2,1,1,2\}\}$ is$3$ $8$ $4$ $2$
User Avatar
3 votes
3 votes
1 answer
4
gatecse asked Dec 17, 2017
1,798 views
ISRO-DEC2017-4
If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log \mid x \mid+\beta x^2+x$ then $\alpha=-6,\beta=\dfrac{-1}{2}$ $\alpha=2,\beta=\dfrac{-1}{2}$ $\alpha=2,\beta=\dfrac{1}{2}$ $\alpha=-6,\beta=\dfrac{1}{2}$
If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log \mid x \mid+\beta x^2+x$ then$\alpha=-6,\beta=\dfrac{-1}{2}$ $\alpha=2,\beta=\dfrac{-1}{2}$ $\alpha=2,\beta=\d...
User Avatar
Link Copied!