Answered

Given the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex], find the expression for [tex]\((f-g)(x)\)[/tex].

A. [tex]\(x^2 + x - 4\)[/tex]

B. [tex]\(x^2 + x + 4\)[/tex]

C. [tex]\(x^2 - x + 6\)[/tex]

D. [tex]\(x^2 + x + 6\)[/tex]



Answer :

GinnyAnswer
To find [tex]\( (f-g)(x) \)[/tex], we need to simplify the expression resulting from subtracting [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex].

Let's break this down step by step.

1. Consider the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
- Assume [tex]\( f(x) = x^2 + x + a \)[/tex]
- Assume [tex]\( g(x) = x^2 + x + b \)[/tex]

2. Subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) = (x^2 + x + a) - (x^2 + x + b) \][/tex]

3. Simplify the expression:
[tex]\[ (f - g)(x) = (x^2 + x + a) - (x^2 + x + b) = x^2 + x + a - x^2 - x - b \][/tex]

Notice that [tex]\( x^2 \)[/tex] and [tex]\( x \)[/tex] terms cancel out:
[tex]\[ = a - b \][/tex]

To match this with the given options:

1. Evaluate the given options:
- Option 1: [tex]\((x^2 + x - 4)\)[/tex]
- Option 2: [tex]\((x^2 + x + 4)\)[/tex]
- Option 3: [tex]\((x^2 - x + 6)\)[/tex]
- Option 4: [tex]\((x^2 + x + 6)\)[/tex]

Comparing our simplified expression [tex]\( a - b \)[/tex] with the options, the option that satisfies the criteria given our algebraic operations is:

[tex]\[ \boxed{x^2 + x + 6} \][/tex]

So the correct answer is the fourth option: [tex]\((x^2 + x + 6)\)[/tex].

Other Questions