Question

Please answer it.. Let f let f:r to r be the identity function. what is f. f and fof.

Answer 1

Here, we are given a function f ,which is defined from R to R. Also, f is said to be the Identity Function.



The Identity Function returns the same output as given in the input. 

That is, if you input some x into f(x), you get the result as x itself. So, the Identity Funtion is:

$\boxed{f \, : \, \mathbb{R} \rightarrow \mathbb{R} \, , \, \, \, f(x)=x}$


As we can see, the Domain of the function is $\mathbb{R}$, and the co-domain as well as range is also $\mathbb{R}$

Now, let us get to fof, which is a composition function.

$fof \\ \\ \\ = f(f(x)) \\ \\ \\ Put \, \, f(x) = x \\ \\ \\ = f(x) \\ \\ \\ = x \\ \\ \\ \\ \implies \boxed{fof = f(x) = x}$

Thus the composition itself is also an identity function.

Now, we can also plot a graph.

Let f(x) = y

Then we have the function as:

f(x) = x
So, y = x
We can plot this, and an image is attached.



$\mathbb{H} \mathfrak{ope \, \, it \, \, helps}$
Purva
Brainly Community

Answer 2

Answer:

1. f.f=x²

2. fof=x

Step-by-step explanation:

f:R to R, identity function

If x is put into f(x),then it results as x

f:R to R,f(x)=x

Domain of function =R

Co-domain of function=R

Range of function =R

1. f.f=f(x).f(x)

=x.x=x²

Thus,f.f=x²

2. fof =f(f(x))

=f(x)=x

fof =x

Thus composition itself is identity function.