Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
132 views
in Sets, Relations and Functions by (93.6k points)
closed by
Let `f : R rarr R` be defined by f(x) = cos (5x+2). Is f invertible? Justify your answer.

1 Answer

0 votes
by (92.3k points)
selected by
 
Best answer
For invertible of f, f must be bijective (i.e, one-one onto).
If `x_(1), x_(2) in R`,
then `f(x_(1))=f(x_(2))`
`implies cos(5x_(1)+2)=cos(5x_(2)+2)`
`implies 5x_(1)+2=2npipm(5x_(2)+2)`
`implies x_(1)nex_(2)`
`therefore` f is not one-one.
But `-1lecos(5x+2)le1`
`therefore -1lef(x)le1`
Range `=[-1,1]subR`
`therefore` f is into mapping.
Hence, the function f(x) is no bijective and so it is not invertible.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...