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Determine the domain and range of (g ○ f)(x) if f(x)=2/x^2 -1 and g(x)=x+1

User Bombo
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1 Answer

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18 votes

Long answer:

The domain is all real numbers except -6 and 0. Hence, domain D: x ≠ –6, 0

Hence the range is all real numbers except -3 and 3. Hence, range R: (–∞, –3) ∪ (3, ∞)

Given the following functions:

First we need to get the composite function f(g(x))

Get the domain

The domain the values of x for which the function exists. The function cannot exists at when x = -6 and x = 0

Hence the domain is all real numbers except -6 and 0. Hence, domain D: x ≠ –6, 0

The range is the value of y for which the function exists. The function cannot exists at when x = -6 and x = 0

Hence the range is all real numbers except -3 and 3. Hence, range R: (–∞, –3) ∪ (3, ∞)

User Krowe
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