Given any two functions f and g, which of the following statements is always true?(1 point)

Question

Responses

If x is in the domain of f, then x must be in the domain of f−g.
If x is in the domain of , f, , then x must be in the domain of , f minus g, .

If x is not in the domain of fg, then x is not in the domain of g.
If x is not in the domain of , StartFraction f over g EndFraction, , then x is not in the domain of , g, .

If x1 is in the domain of f and x2 is in the domain of g, then the product, x1x2, must be in the domain of fg.
If , x subscript 1 baseline, is in the domain of , f, and , , x subscript 2 baseline, is in the domain of , g, , , then the product,, , x subscript 1 baseline x subscript 2 baseline, , must be in the domain of , f g, .

If x is in the domain of f+g, then x must be in the domain of f and x must be in the domain of g.
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What is (f−g)(x)?(1 point)
Responses

It is the difference of two functions, f(x)−g(x) times x.
It is the difference of two functions, , f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis, times x.

It is the product of two functions, f(x)⋅g(x).
It is the product of two functions, , f left parenthesis x right parenthesis times g left parenthesis x right parenthesis, .

It is the difference of two functions, f(x)−g(x).
It is the difference of two functions, , f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis, .

It is the difference of two functions, g(x)−f(x).
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Find fg and explain the domain for the function.

f(x)=2x2−25x+72, g(x)=x−8

(1 point)
Responses

The function is (fg)(x)=2x+9. The domain of fg is all real numbers because the domain of f and the domain of g are both all real numbers.
, The function is , left parenthesis StartFraction f over g EndFraction right parenthesis left parenthesis x right parenthesis equals 2 x plus 9, . The domain of , StartFraction f over g EndFraction, is all real numbers , , because the domain of f and the domain of g are both all real numbers.

The function is (fg)(x)=2x−9. The domain of fg is all real numbers except for x=8 because the denominator is 0 when x=8.
The function is , left parenthesis StartFraction f over g EndFraction right parenthesis left parenthesis x right parenthesis equals 2 x minus 9, . The domain of , StartFraction f over g EndFraction, is all real numbers except for , x equals 8, because the denominator is 0 when , x equals 8, .

The function is (fg)(x)=2x+9. The domain of fg is all real numbers except for x=8 and x=92 because the denominator is 0 when x=8 or when x=92.
, The function is , left parenthesis StartFraction f over g EndFraction right parenthesis left parenthesis x right parenthesis equals 2 x plus 9, . The domain of , StartFraction f over g EndFraction, is all real numbers except for , x equals 8, and , x equals 9 halves, because the denominator is 0 when , x equals 8, or when , x equals 9 halves, , .

The function is (fg)(x)=2x−9. The domain of fg is all real numbers because the domain of f and the domain of g are both all real numbers.
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Let f(x)=4x+5−−−−−√ and g(x)=25x−9−−−−−−√. Evaluate the expression.

(f−g)(1)

(1 point)
Responses

(f−g)(1)=1
left parenthesis f minus g right parenthesis left parenthesis 1 right parenthesis equals 1

(f−g)(1)=7
left parenthesis f minus g right parenthesis left parenthesis 1 right parenthesis equals 7

(f−g)(1)=−7
left parenthesis f minus g right parenthesis left parenthesis 1 right parenthesis equals negative 7

(f−g)(1)=−1
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Scarlett sells designer ponchos. The revenue, R, she makes from selling a batch of n ponchos is given by the function R(n)=20n, and the expenses, E, that she incurs from producing a batch of n ponchos is given by the function E(n)=10n√. Explain whether Scarlett earns a profit from producing and selling a batch of 9 ponchos.(1 point)
Responses

Scarlett earns a profit because R(10)E(10)=6.
Scarlett earns a profit because , Start Fraction upper r left parenthesis 10 right parenthesis over upper e left parenthesis 10 right parenthesis End Fraction equals 6, .

Scarlett earns a profit because R(10)−E(10)=150.
Scarlett earns a profit because , upper r left parenthesis 10 right parenthesis minus upper e left parenthesis 10 right parenthesis equals 150, .

Scarlett earns a profit because R(10)+E(10)=210.
Scarlett earns a profit because , upper r left parenthesis 10 right parenthesis plus upper e left parenthesis 10 right parenthesis equals 210, .

Scarlett does not earn a profit because E(10)−R(10)=−150.