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1. Find [tex]\((f-g)(x)\)[/tex] if [tex]\(f(x) = -2x + 4\)[/tex] and [tex]\(g(x) = x^2 - 3x + 5\)[/tex].

A. [tex]\((f-g)(x) = x^2 - 5x + 9\)[/tex]

B. [tex]\((f-g)(x) = x^2 + 5x - 9\)[/tex]

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

D. [tex]\((f-g)(x) = -x^2 + x - 1\)[/tex]

Sagot :

GinnyAnsweridn
To find [tex]\((f - g)(x)\)[/tex] given the functions [tex]\(f(x) = -2x + 4\)[/tex] and [tex]\(g(x) = x^2 - 3x + 5\)[/tex], follow these steps:

1. Express [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = -2x + 4 \][/tex]
[tex]\[ g(x) = x^2 - 3x + 5 \][/tex]

2. Define [tex]\((f - g)(x)\)[/tex] as the difference between [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]

3. Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:
[tex]\[ (f - g)(x) = (-2x + 4) - (x^2 - 3x + 5) \][/tex]

4. Distribute the negative sign through the second term:
[tex]\[ (f - g)(x) = -2x + 4 - x^2 + 3x - 5 \][/tex]

5. Combine like terms:
[tex]\[ -x^2 + (-2x + 3x) + (4 - 5) \][/tex]
[tex]\[ -x^2 + x - 1 \][/tex]

Therefore, the correct expression for [tex]\((f - g)(x)\)[/tex] is:
[tex]\[ (f - g)(x) = -x^2 + x - 1 \][/tex]

So, the correct answer is:
[tex]\((f - g)(x) = -x^2 + x - 1\)[/tex].
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