8. Which graph correctly shows the solution of the compound inequality 3x > 3 and 9x < 54?
1 answer:
The answer is shown in the image attached
Compound inequality is an inequality made up of two inequalities joined together using 'or' or 'and'.
Given the inequalities 3x > 3 and 9x < 54. Solving both inequalities gives:
3x > 3 and 9x < 54
x > 1 and x < 6
x > 1 is equivalent to x ∈ (1, ∞)
x < 6 is equivalent to x ∈ (-∞, 6)
Therefore, combining the two inequalities together gives:
(1, ∞) ∩ (-∞, 6) = (1, 6)
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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.