Question

Let f: R → R, be the identity function f (x) = x. Then f is:
a) continuous but not open.
b) open but not continuous
c) homeomorphism
d) neither open nor continuous​

Answer 1

Answer:

neither open nor continuous

Answer 2

Answer:

The correct option is (a) continuous but not open.

Concept:

An identity function in mathematics is a function that consistently returns the value that was used as its argument, unchanged. It is also referred to as an identity relation, identity map, or identity transformation. That is, for all values of X to which f may be applied, the equality f(X) = X holds true when f is the identity function.

Step-by-step explanation:

Given:

Let f: R → $R_{i}$ be the identity function f (x) = x.

Find:

Let f: R → $R_{i}$ be the identity function f (x) = x. Then f is:

Solution:

We know that the Identity function is a Continuous

Given, that f = R → $R_{i}$   $R_{i}$ is a Continuous function,

               f(x) = x

It is both open and close. Hence option (a) is correct

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