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Combine functions using subtraction.

If [tex]\( g(x) = x^2 + 4x \)[/tex] and [tex]\( h(x) = 3x - 5 \)[/tex], what is [tex]\( g(x) - h(x) \)[/tex]?

A. [tex]\( g(x) - h(x) = x^2 + x - 5 \)[/tex]

B. [tex]\( g(x) - h(x) = x^2 + x + 5 \)[/tex]

C. [tex]\( g(x) - h(x) = x^2 + 7x - 5 \)[/tex]

D. [tex]\( g(x) - h(x) = x^2 + 7x + 5 \)[/tex]

Sagot :

GinnyAnswer
To find [tex]\( g(x) - h(x) \)[/tex] given the functions [tex]\( g(x) \)[/tex] and [tex]\( h(x) \)[/tex], follow these steps:

1. Write down the given functions:
[tex]\( g(x) = x^2 + 4x \)[/tex]
[tex]\( h(x) = 3x - 5 \)[/tex]

2. Set up the expression for [tex]\( g(x) - h(x) \)[/tex]:
[tex]\( g(x) - h(x) = (x^2 + 4x) - (3x - 5) \)[/tex]

3. Distribute the negative sign across the terms in [tex]\( h(x) \)[/tex]:
[tex]\( - (3x - 5) = -3x + 5 \)[/tex]

4. Combine the expressions:
[tex]\( g(x) - h(x) = x^2 + 4x - 3x + 5 \)[/tex]

5. Simplify by combining like terms:
Combine the [tex]\( x \)[/tex]-terms: [tex]\( 4x - 3x = x \)[/tex]
So, [tex]\( g(x) - h(x) = x^2 + x + 5 \)[/tex]

Therefore, the correct expression for [tex]\( g(x) - h(x) \)[/tex] is:
[tex]\[ g(x) - h(x) = x^2 + x + 5 \][/tex]

The correct answer is:
[tex]\[ g(x) - h(x) = x^2 + x + 5 \][/tex]
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