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