1. Which polynomial does the model represent?
1 answer:
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Answer:
<em>The last is the correct option</em>
<em>"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"</em>
Step-by-step explanation:
<u>Domain and Range of Functions</u>
Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.
We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then
is the composite function of f and g.
We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.
Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.
Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.
Thus, the domain of is
All real numbers except x=7 and those where f(x)=-3
The last is the correct option