Function Operations Answers

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If and d(x) = x + 3, what is the domain of (cd)(x)?

all real values of x

all real values of x except x = 2

all real values of x except x = –3

all real values of x except x = 2 and x = –3

Which expression is equivalent to (f + g)(4)?

f(4) + g(4)

f(x) + g(4)

f(4 + g(4))

4(f(x) + g(x))

If p(x) = x2 – 1 and , which expression is equivalent to (p – q)(x)?

5(x – 1) – x2 – 1

(5x – 1) – (x2 – 1)

(x2 – 1) – 5(x – 1)

(x2 – 1) – 5x – 1

If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true?

The leading coefficients of f(x) and g(x) are opposites.

The leading coefficients of f(x) and g(x) are opposite reciprocals.

The leading coefficients of f(x) and g(x) are the same.

The leading coefficients of f(x) and g(x) are reciprocals.

The graphs of f(x) and g(x) are shown below. Which of the following is the graph of (g – f)(x)?

On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)

On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).

On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).

On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).

If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?

StartFraction 3 (6) minus 1 Over 2 (6) + 1 EndFraction

StartFraction (6) Over 2 (6) + 1 EndFraction

StartFraction 36 minus 1 Over 26 + 1 EndFraction

StartFraction (6) minus 1 Over (6) + 1 EndFraction

If f(x) = 3 – 2x and , what is the value of ?

–169

–1

104

If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

–4

–2

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