Let f(x)=3x-6 and g(x)=x-2 find f(g(5))-ie. (f • g)(5) and its domain
1 answer:
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.
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The number of zeros of the quadratic functions, considering their discriminant, is given as follows:
- discriminant = 0: 1 Real number solution.
- discriminant = -36: 0 Real number solutions.
- discriminant = 3: 2 Real number solutions.
- discriminant = 2: 2 Real number solutions.
- discriminant = 100: 2 Real number solutions.
- discriminant = -4: 0 Real number solutions.
A quadratic equation is modeled by:
The discriminant is:
The solutions are as follows:
- If
, it has 2 real solutions.
- If
, it has 1 real solutions.
- If
, it has 0 real solutions.
Hence, for the given values of the discriminant, we have that:
- discriminant = 0: 1 Real number solution.
- discriminant = -36: 0 Real number solutions.
- discriminant = 3: 2 Real number solutions.
- discriminant = 2: 2 Real number solutions.
- discriminant = 100: 2 Real number solutions.
- discriminant = -4: 0 Real number solutions.
More can be learned about quadratic functions at brainly.com/question/24737967
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