Simplify.
2 answers:
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Answer:
Domain is (0,∞)
Range is (45, ∞)
Step-by-step explanation:
Let x represents the number of persons and f(x) represents the average cost per person,
∵ Fixed cost = $ 2500
Also, additional cost is $ 45 per person,
So, the total cost for x persons ( in dollars ) = fixed deposit + additional cost for x persons,
= 2500 + 45x
Which is a rational function,
∵ A rational function is defined for all real numbers except those for denominator = 0
Denominator of f(x) = x
So, f(x) is defined for all real numbers except x ≠ 0,
Now, the cost can not be negative,
⇒ x > 0
Hence, the domain for f(x) is (0, ∞)
Again,
If
So, 45 < f(x) < ∞
i.e., range of f(x) is (45, ∞)