Question

using a graph demonstrate a function which is one-one but not onto​

Answer 1

SOLUTION

TO DETERMINE

using a graph demonstrate a function which is one-one but not onto

EVALUATION

We know that for two non empty sets A and B a mapping f from A to B is a rule that assigns to each element x of A a definite element y in B

A mapping f : A B is said to be one to one if x ≠ x' implies f(x) = f(x')

Again f is said to be onto if each element y of B has at least one preimage

Let us consider the sets

A = { 1 , 2 , 3 } and B = { a , b , c , d }

Define mapping f : A B such that

f(1) = b , f(2) = a , f(3) = d

Then f is one to one

But the element c in the codomain set B has no preimage

So f is not onto

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Learn more from Brainly :-

$1.$ identify distinction between a relation and a function with suitable examples and illustrate graphically

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2. Represent all possible one-one functions from the set A = {1, 2} to the set B = {3,4,5) using arrow diagram.

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Answer 2

f ( x )  = $e^{x}$

Explanation:

in an 'onto' function, every  x -value is mapped to a  y − value.  

in a one-to-one function, every  y -value is mapped to at most one  x - value.

this means that in a one-to-one function, not every  x -value in the domain must be mapped on the graph. it only means that no  y -value can be mapped twice.

the graph of $e^{x}$  is one-to-one.  there is no more than one  x -value for each  y -value, and there is no more than one  y -value for each  x-value.

this can be shown using the horizontal line test: a horizontal line, drawn anywhere on the graph (i.e. of any  y -value), will not intersect with a one-to-one function more than once (if at all).

the graph of  $e^{x}$ not every  y -value is mapped on the graph;  

$e^{x}$ can never be  0  or below.  y = 0  is the horizontal asymptote of the graph.