Question

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

Answer 1

Long answer:

The domain is all real numbers except -6 and 0. Hence, domain D: {x ∈ ℝ| 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 ∈ ℝ| 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, ∞)