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Given h(x) = (3x-4), f(x) = (7x+2), and g(x) = (9x+1), which of the following is equivalent to 2x+3?

A. h(x) + g(x)
B. g(x) + f(x)
C. g(x) * h(x)
D. h(x) - g(x)

Respuesta :

A) h(x)+g(x)=(3x-4)+(9x+1)=12x-3
B) g(x) + f(x)=(9x+1)+(7x+2)=16x+3
C) g(x)*h(x)= (9x+1)(3x-4)=27x²+3x-36x-4=27x²-33x-4
D)h(x)-g(x)=(3x-4)-(9x+1)= - 6x -5

if f(x)= -7x +2
B) g(x)+f(x)=(9x+1)+(-7x+2)=9x-7x+1+2=2x+3
answer B

The only option that is equivalent to 2x + 3 is;

Option B; g(x) + f(x)

We are given;

h(x) = (3x - 4)

f(x) = (-7x + 2) (The correct one has negative sign before the 7)

g(x) = (9x + 1)

Option A; h(x) + g(x)

Plugging in the relevant equations gives;

(3x - 4) + (9x + 1)

⇒ 3x - 4 + 9x + 1

⇒ 12x - 3

Option B; g(x) + f(x)

Plugging in the relevant equations gives;

(9x + 1) + (-7x + 2)

⇒ 9x + 1 - 7x + 2

⇒ 2x + 3

Option C;  g(x) * h(x)

Plugging in the relevant equations gives;

(9x + 1) ×  (3x - 4)

⇒ 27x² + 3x - 36x - 4

⇒ 27x² - 33x - 4

Option D: h(x) - g(x)

Plugging in the relevant equations gives;

(3x - 4) - (9x + 1)

⇒ -6x - 5

The only option that corresponds to 2x + 3 is Option B.

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