If R be the set of real numbers and f : R → R is defined by f(x) = e^x, then f is

Given:

R be the set of real numbers.

f : R → R is defined by f(x) = ex

Concept:

Surjective function :

A function R is a surjective function such that every element y can be mapped from an element x so that f(x) =y.

Injective function :

A function R is an injective function that maps distinct elements of its domain to distinct elements i.e., f(x₁) = f(x₂), ⇒ x₁ = x₂.

Bijective :

A function is said to be bijective, if a function R : A→B satisfies the properties of both the injective function & surjective function.

Solution:

for negative y - axis we do not have any pre-image

Therefore f(x) is injective.

Since f(x) is satisfying the properties of the injective functions only.

So f(x) is a injective function.