Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To solve the problems, we need to evaluate the compositions of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] at the given points.
Given:
[tex]\[ f(x) = x^2 - 6x \][/tex]
[tex]\[ g(x) = x + 7 \][/tex]
Let's evaluate each part step-by-step.
### (a) [tex]\((f \circ g)(1)\)[/tex]
1. First, find [tex]\(g(1)\)[/tex]:
[tex]\[ g(1) = 1 + 7 = 8 \][/tex]
2. Next, use this result as the input to [tex]\(f\)[/tex]:
[tex]\[ f(g(1)) = f(8) \][/tex]
3. Now, evaluate [tex]\(f(8)\)[/tex]:
[tex]\[ f(8) = 8^2 - 6 \cdot 8 = 64 - 48 = 16 \][/tex]
Thus:
[tex]\[ (f \circ g)(1) = 16 \][/tex]
### (b) [tex]\((g \circ f)(1)\)[/tex]
1. First, find [tex]\(f(1)\)[/tex]:
[tex]\[ f(1) = 1^2 - 6 \cdot 1 = 1 - 6 = -5 \][/tex]
2. Next, use this result as the input to [tex]\(g\)[/tex]:
[tex]\[ g(f(1)) = g(-5) \][/tex]
3. Now, evaluate [tex]\(g(-5)\)[/tex]:
[tex]\[ g(-5) = -5 + 7 = 2 \][/tex]
Thus:
[tex]\[ (g \circ f)(1) = 2 \][/tex]
### Final Answer
So the evaluated results are:
(a) [tex]\((f \circ g)(1) = 16\)[/tex]
(b) [tex]\((g \circ f)(1) = 2\)[/tex]
Given:
[tex]\[ f(x) = x^2 - 6x \][/tex]
[tex]\[ g(x) = x + 7 \][/tex]
Let's evaluate each part step-by-step.
### (a) [tex]\((f \circ g)(1)\)[/tex]
1. First, find [tex]\(g(1)\)[/tex]:
[tex]\[ g(1) = 1 + 7 = 8 \][/tex]
2. Next, use this result as the input to [tex]\(f\)[/tex]:
[tex]\[ f(g(1)) = f(8) \][/tex]
3. Now, evaluate [tex]\(f(8)\)[/tex]:
[tex]\[ f(8) = 8^2 - 6 \cdot 8 = 64 - 48 = 16 \][/tex]
Thus:
[tex]\[ (f \circ g)(1) = 16 \][/tex]
### (b) [tex]\((g \circ f)(1)\)[/tex]
1. First, find [tex]\(f(1)\)[/tex]:
[tex]\[ f(1) = 1^2 - 6 \cdot 1 = 1 - 6 = -5 \][/tex]
2. Next, use this result as the input to [tex]\(g\)[/tex]:
[tex]\[ g(f(1)) = g(-5) \][/tex]
3. Now, evaluate [tex]\(g(-5)\)[/tex]:
[tex]\[ g(-5) = -5 + 7 = 2 \][/tex]
Thus:
[tex]\[ (g \circ f)(1) = 2 \][/tex]
### Final Answer
So the evaluated results are:
(a) [tex]\((f \circ g)(1) = 16\)[/tex]
(b) [tex]\((g \circ f)(1) = 2\)[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.