Let f, g: R → R be defined by f(x) = 2x + 1

Question:

Let f, g: R → R be defined by f(x) = 2x + 1 and g (x) = x2 – 2, ∀ x ∈ R, respectively. Then, find g o f.

Solution:

Given,

f(x) = 2x + 1 and g (x) = x2 – 2, ∀ x ∈ R

Thus, g o f = g (f (x))

= g (2x + 1)

= (2x + 1)2 – 2

= 4x2 + 4x + 1 – 2

= 4x2 + 4x – 1

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