Q. 85.0( 2 Votes )

Show that the fun

Answer :

To prove: function is many-one into


Given: f : R R : f(x) = 1 + x2


We have,


f(x) = 1 + x2


For, f(x1) = f(x2)


1 + x12 = 1 + x22


x12 = x22


x12 - x22 = 0


(x1 – x2) (x1 + x2) = 0


x1 = x2 or, x1 = –x2


Clearly x1 has more than one image


f(x) is many-one


f(x) = 1 + x2


Let f(x) = y such that


y = 1 + x2


x2 = y – 1



If y = 3, as


Then x will be undefined as we can’t place the negative value under the square root


Hence f(x) is into


Hence Proved


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Fill in theMathematics - Exemplar

Let f : [2, ∞) <sMathematics - Exemplar

Let f : N Mathematics - Exemplar

Fill in theMathematics - Exemplar

Let f :R →<Mathematics - Exemplar

Let f : [0, 1] <sMathematics - Exemplar

Which of the follMathematics - Exemplar