Mathematics, 09.07.2019 03:30 kendall984

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.)

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Answer from: amcalfie

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 (-∞, ∞)

Answer from: kloey908

(f+g)(x)=x-3+x^2 ; Domain = (-∞, ∞)

(f-g)(x)=x-3-x^2 ; Domain = (-∞, ∞)

(fg)(x)=x^3-3x^2 ; Domain = (-∞, ∞)

$(\frac{f}{g})(x)=\frac{x-3}{x^2}$ ; Domain = (-∞,0)∪(0, ∞)

Step-by-step explanation:

The given functions are

f(x)=x-3

g(x)=x^2

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

Substitute the values of the given functions.

(f+g)(x)=(x-3)+x^2

(f+g)(x)=x-3+x^2

The function (f+g)(x)=x-3+x^2 is a polynomial which is defined for all real values x.

Domain of (f+g)(x) = (-∞, ∞)

(f-g)(x)=f(x)-g(x)

Substitute the values of the given functions.

(f-g)(x)=(x-3)-x^2

(f-g)(x)=x-3-x^2

The function (f-g)(x)=x-3-x^2 is a polynomial which is defined for all real values x.

Domain of (f-g)(x) = (-∞, ∞)

(fg)(x)=f(x)g(x)

Substitute the values of the given functions.

(fg)(x)=(x-3)x^2

(fg)(x)=x^3-3x^2

The function (fg)(x)=x^3-3x^2 is a polynomial which is defined for all real values x.

Domain of (fg)(x) = (-∞, ∞)

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$

Substitute the values of the given functions.

$(\frac{f}{g})(x)=\frac{x-3}{x^2}$

The function $(\frac{f}{g})(x)=\frac{x-3}{x^2}$ is a rational function which is defined for all real values x except 0.

Domain of (f/g)(x) = (-∞,0)∪(0, ∞)

Answer from: Quest

1 3 5

step-by-step explanation:

i took the test: )

Answer from: Quest

gimmee one of those gold crowns!

~coco

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Consider the following functions. f(x) = x − 3, g(x) = x2 find (f + g)(x). find the domain of (f + g...

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