From simple questions to complex issues, IDNLearn.com has the answers you need. Join our knowledgeable community and get detailed, reliable answers to all your questions.
Sagot :
Let's solve each part of the question step-by-step.
### (a) Find [tex]\((f + g)(x)\)[/tex]
Given:
[tex]\[ (f + g)(x) = 9x + 3 \][/tex]
The expression [tex]\((f + g)(x)\)[/tex] is already simplified since it is given as [tex]\(9x + 3\)[/tex].
To check the domain of [tex]\((f + g)\)[/tex]:
Since [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] are linear functions and their sum [tex]\(9x + 3\)[/tex] is also a linear function, the domain of a linear function is all real numbers.
Thus, the domain of [tex]\((f + g)\)[/tex] is:
B. The domain is [tex]\(\{ x \mid x \text{ is any real number} \}\)[/tex]
### (b) Find [tex]\((f - g)(x)\)[/tex]
To find [tex]\((f - g)(x)\)[/tex]:
Given that [tex]\(f(x) = 4.5x + 1.5\)[/tex] and [tex]\(g(x) = 4.5x + 1.5\)[/tex] (determined from the sum provided in the question),
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substituting the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f - g)(x) = (4.5x + 1.5) - (4.5x + 1.5) \][/tex]
Simplifying this expression:
[tex]\[ (f - g)(x) = 4.5x + 1.5 - 4.5x - 1.5 \][/tex]
[tex]\[ (f - g)(x) = 0 \][/tex]
Thus, the simplified form of [tex]\((f - g)(x)\)[/tex] is:
[tex]\((f - g)(x) = 0\)[/tex]
### Summary
1. [tex]\((f + g)(x) = 9x + 3\)[/tex]
2. The domain of [tex]\((f + g)\)[/tex] is [tex]\(\{ x \mid x \text{ is any real number} \}\)[/tex]
3. [tex]\((f - g)(x) = 0\)[/tex]
### (a) Find [tex]\((f + g)(x)\)[/tex]
Given:
[tex]\[ (f + g)(x) = 9x + 3 \][/tex]
The expression [tex]\((f + g)(x)\)[/tex] is already simplified since it is given as [tex]\(9x + 3\)[/tex].
To check the domain of [tex]\((f + g)\)[/tex]:
Since [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] are linear functions and their sum [tex]\(9x + 3\)[/tex] is also a linear function, the domain of a linear function is all real numbers.
Thus, the domain of [tex]\((f + g)\)[/tex] is:
B. The domain is [tex]\(\{ x \mid x \text{ is any real number} \}\)[/tex]
### (b) Find [tex]\((f - g)(x)\)[/tex]
To find [tex]\((f - g)(x)\)[/tex]:
Given that [tex]\(f(x) = 4.5x + 1.5\)[/tex] and [tex]\(g(x) = 4.5x + 1.5\)[/tex] (determined from the sum provided in the question),
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substituting the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f - g)(x) = (4.5x + 1.5) - (4.5x + 1.5) \][/tex]
Simplifying this expression:
[tex]\[ (f - g)(x) = 4.5x + 1.5 - 4.5x - 1.5 \][/tex]
[tex]\[ (f - g)(x) = 0 \][/tex]
Thus, the simplified form of [tex]\((f - g)(x)\)[/tex] is:
[tex]\((f - g)(x) = 0\)[/tex]
### Summary
1. [tex]\((f + g)(x) = 9x + 3\)[/tex]
2. The domain of [tex]\((f + g)\)[/tex] is [tex]\(\{ x \mid x \text{ is any real number} \}\)[/tex]
3. [tex]\((f - g)(x) = 0\)[/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.