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Question
Let A, B, C ⊆ N and a function f: A → B be defined by f(x) = 2x + 1 and g: B → C be defined by g(x) = x2. Find the range of fog and gof.
Solution
f(x) = 2x + 1, g(x) = x2
fog = f[g(x)]
= f(x2)
= 2x2 + 1
2x2 + 1 ∈ N
gof = g[f(x)]
= g(2x + 1)
gof = (2x + 1)2
(2x + 1)2 ∈ N
Range = `{y/y = 2x^2 + 1, x ∈ N}`;
`{y/y = (2x + 1)^2, x ∈ N)`
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