Answer:

Let us calculate ,

Clearly, the range of is not a subset of the domain of

Let us calculate

Clearly, the range of is a subset of the domain of

Let us calculate

Clearly, the range of is a subset of the domain of

Let us calculate

Clearly, the range of is a subset of the domain of

Let us calculate

Clearly, range of is a subset of domain of

Let us compute

Clearly, range of is a subset of domain of

Let us compute the

Clearly, the range of is not a subset of the domain of

Let us compute the

Let us compute the

Set of the domain of

Let us compute the

Clearly, the range of is a subset of the domain of

Let us compute the

Clearly, the range of is a subset of the domain of

Let us compute

Clearly, the range of is a subset of the domain of

Let us compute the

Clearly, the range of is a subset of the domain of

Let us compute the

Clearly, the range of is a subset of the domain of

For range of

Let us compute the

Clearly, the range of is a subset of the domain of

Now we have to compute

Clearly, the range of is a subset of the domain of

Answer:

Answer:

Question 4: If be two real functions, then describe each of the following functions:

Answer:

The function and are polynomials.

Question 5: If be two real functions, then describe Are these equal functions?

Answer:

Clearly, the range of is a subset of the domain of

Clearly, the range of is a subset of the domain of

Hence they are not equal functions.

Question 6: Let be real functions given by

Answer:

Question 7: Let be any real function and let be a function given by Prove that

Answer:

Answer:

Computation of

Clearly, the range of is not a subset of the domain of

Computation of

Clearly, the range of is a subset of the domain of

Answer:

We know that

Computation of

Clearly, the range of is a subset of the domain of

Computation of

Clearly, the range of is not a subset of the domain of

Answer:

Computation of

Range of g is not a subset of the domain of f

Computation of

Range of f is a subset of the domain of

Question 11: Let be a real function given by Find each of the following:

Also, show that

Answer:

Range of f is not a subset of the domain of f.

Range of f is not a subset of the domain of fof.

Answer:

This can be written as

Answer:

Therefore,

Therefore, g(f(x)) = gof = 0