# Show that the exp

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 Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.

So, is Surjection iff for each , there exists such that f(a) = b

Now, given by f(x) = ex

Check for Injectivity:

Let x,y be elements belongs to R i.e such that

So, from definition

f(x) = f(y)

ex = ey ex – y = 1

ex – y = e0

x – y = 0

x = y

Hence f is One – One function

Check for Surjectivity:

Here range of f = (0,∞) ≠ R

Therefore f is not onto

Now if co – domain is replaced by R0 + (set of all positive real numbers) i.e (0,∞) then f becomes an onto function.

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 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