Answer:
Option D
Step-by-step explanation:
We have to find the value of the composite function (h o k)(2).
Since, (h o k)(x) = h[k(x)]
(h o k)(2) = h[k(2)]
From the picture attached,
At x = 2
k(2) = (-2)
Therefore, h[k(2)] = h(-2)
Since, h(x) =
Therefore, h(-2) =
= -3
(h o k)(2) = -3 is the answer.
Option (D) is the correct option.
Answer:
FALSE, (2, 9) is not a solution to the set of inequalities given.
Step-by-step explanation:
Simply replace x by 2 and y by 9 in the inequalities and see if the inequality is true or not:
irst inequality:
so thi inequality is verified as true since 9 is larger or equal than 8
Now the second inequality:
This is FALSE since 9 is larger than 4 (not smaller)
Therefore the answer to the question is FALSE, (2, 9) is not a solution to the set of inequalities given.
Solution for f(g(5)):
The notation f(g(5)) or (f • g)(5) means that we first plug 5 into the function g(x), simplify, then plug the answer that we got to f(x). We will do this step-by-step:
Step 1: Plugging 5 to g(x)
Step 2: Plugging the answer to f(x)
ANSWER: f(g(5)) is equal to 3.
Domain:
For the function f(g(x)), we can find the domain by analyzing the domains of each individual functions separately and excluding certain values depending on the restrictions from the outermost function.
However, since both functions have all real numbers as its domain, we will not need to do any exclusion anymore.
ANSWER: The domain of the function is all real numbers.