Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Answer:
(g-h)(x) = x+3-2x2
(g+h)(x) = x+ 3 +2x2
to evaluate, replace x by -3 and compute, carefully.
Answer:
[tex](g-h)(x) = 3x+11[/tex]
[tex](g+h)(x) = 5x+1[/tex]
[tex](g-h)(3) =20[/tex]
[tex](g+h)(3) =16[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}g(x)=4x+6\\h(x)=x-5\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Therefore, the composite function (g-h)(x) means subtract function h(x) from function g(x). Similarly, (g+h)(x) means to add function h(x) to function g(x).
[tex]\begin{aligned}(g-h)(x) & = g(x)-h(x)\\& = (4x+6)-(x-5)\\& = 4x+6-x+5\\& = 4x-x+6+5\\& = 3x+11\end{aligned}[/tex]
[tex]\begin{aligned}(g+h)(x) & = g(x)+h(x)\\& = (4x+6)+(x-5)\\& = 4x+6+x-5\\& = 4x+x+6-5\\& = 5x+1\end{aligned}[/tex]
To evaluate both composite functions when x = 3, simply substitute x = 3 into the found composite functions:
[tex]\begin{aligned}(g-h)(3) & = 3(3)+11\\& = 9+11\\&=20\end{aligned}[/tex]
[tex]\begin{aligned}(g+h)(3) & = 5(3)+1\\& = 15+11\\&=16\end{aligned}[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.