Find each of the following functions. f(x) = 3 − x , g(x) = x2 − 4 (a) f + g state the domain of the function. (enter your answer using interval notation.) (b) f − g state the domain of the function. (enter your answer using interval notation.) (c) fg state the domain of the function. (enter your answer using interval notation.) (d) f/g state the domain of the function. (enter your answer using interval notation.)

(a) ;  Domain = (-∞,∞)

(b) ;  Domain = (-∞,∞)

(c) ;  Domain = (-∞,∞)

(d) ; Domain = (-∞,-2)∪(-2,2)∪(2,∞)

Step-by-step explanation:

The given functions are

(a)

We need to find the function f+g.

It is a polynomial and domain of a polynomial is all real numbers.

Domain = (-∞,∞)

(b)

We need to find the function f-g.

It is a polynomial. So,

Domain = (-∞,∞)

(c)

We need to find the function fg.

It is a polynomial. So,

Domain = (-∞,∞)

(d)

We need to find the function f/g.

It is a rational function. Domain of a rational function is all real except those values at which the denominator is equal to 0.

Equate denominator equal to 0.

Taking square both sides.

The function is not defined for x=-2 and x=2. So, domain of f/g is all real numbers except -2 and 2.

Domain = (-∞,-2)∪(-2,2)∪(2,∞)

Answer with Step-by-step explanation:

We are given that

We have to find the

a.Domain of f+g

Domain of f(x)=()

Suppose y=g(x)=

Therefore,

Domain of

Range of

Range of =Domain of g(x)=

Domain of (f+g)(x)=[0,)

Because domain of sum of two function is the intersection of domain of given functions.

Similar, domain of (f-g)(x)=[0,)

Because domain of difference of two function is the intersection of domain of given functions.

Similarly , domain of fg(x)=[0,)

Because domain of product of two function is the intersection of domain of given functions.

Function is not define at x=2 and x=-2

Therefore, domain of =R-{-2,2}=