Q. 195.0( 1 Vote )

Show that if f1 and f2 are one – one maps from R to R, then the product f1 × f2 : R R defined by (f1 × f2)(x) = f1(x)f2(x) need not be one – one.

Answer :

TIP: One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.


So, is One – One function


a≠b


f(a)≠f(b) for all


f(a) = f(b)


a = b for all


Let, f1: R R and f2: R R are two functions given by


f1(x) = x


f2(x) = x


From above function it is clear that both are One – One functions


Now, f1×f2 : R Rgiven by


(f1×f2 )(x) = f1(x)×f2(x) = x2


(f1×f2 )(x) = x2


Also,


f(1) = 1 = f( – 1)


Therefore,


f is not One – One


f1×f2 : R R is not One – One function.


Hence Proved


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 01Functions - 01Functions - 0152 mins
Functions - 10Functions - 10Functions - 1047 mins
Functions - 05Functions - 05Functions - 0558 mins
Functions - 07Functions - 07Functions - 0748 mins
Functions - 02Functions - 02Functions - 0253 mins
Functions - 03Functions - 03Functions - 0361 mins
Functions - 08Functions - 08Functions - 0840 mins
Functions - 12Functions - 12Functions - 1252 mins
Functions - 04Functions - 04Functions - 0460 mins
Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 0161 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses