Consider the following functions. f(x) = x − 3, g(x) = x2 find (f + g)(x). find the domain of (f + g)(x). (enter your answer using interval notation.) find (f − g)(x). find the domain of (f − g)(x). (enter your answer using interval notation.) find (fg)(x). find the domain of (fg)(x). (enter your answer using interval notation.) find f g (x). find the domain of f g (x). (enter your answer using interval notation.)

1) (f + g)(x) : Domain (-∞, ∞)

2) (f - g)(x) : Domain (-∞, ∞)

3) (fg)(x) : Domain (-∞, ∞)

4) (f×g)(x) : Domain (-∞, ∞)

Step-by-step explanation:

Since given functions are f(x) = x - 3 and g(x) = x²

Then (f + g)(x) = f(x) + g(x)

                      = (x - 3) + x²

Since for every of x the given function is defined

Therefor, domain of (f + g)(x) will be defined by (-∞, ∞).

Since, (f - g)(x) = f(x) - g(x)

Now we put the values of f(x) and g(x)

(f - g)(x) = (x - 3) - x²

Since for every value of x, (f - g)(x) is defined.

Therefor, domain of (f - g)(x) will be (-∞, ∞)

SInce, (fg)(x) = f [ g(x) ]

Now f{ g(x) ] = (x²) - 3

                    = x² - 3

Again this function is defined for every value of x.

Therefore, domain of f[ g(x) ] will be (-∞, ∞).

At the last we have to find (f×g)(x) = f(x)×g(x)

                                                        = (x - 3)(x²)

Since this function is defined for all values of x

Therefore, domain of (f×g)(x) will be (-∞, ∞)

; Domain = (-∞, ∞)

; Domain = (-∞, ∞)

; Domain = (-∞, ∞)

; Domain = (-∞,0)∪(0, ∞)

Step-by-step explanation:

The given functions are

1.

Substitute the values of the given functions.

The function is a polynomial which is defined for all real values x.

Domain of (f+g)(x) = (-∞, ∞)

2.

Substitute the values of the given functions.

The function is a polynomial which is defined for all real values x.

Domain of (f-g)(x) = (-∞, ∞)

3.

Substitute the values of the given functions.

The function is a polynomial which is defined for all real values x.

Domain of (fg)(x) = (-∞, ∞)

4.

Substitute the values of the given functions.

The function is a rational function which is defined for all real values x except 0.

Domain of (f/g)(x) = (-∞,0)∪(0, ∞)

step-by-step explanation:

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