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(a + b)^2 Expansion and Visualisation

If the functi...

Question

If the functions $f : R \to R$ and $g : R \to R$ be defined by $f (x) = 2 x + 1, g (x) = x^{2} - 2$ . Find the formulate for g o f and f o g.

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Solution

$f : R ⟶ R g : R ⟶ R f (x) = 2 x + 1, g (x) = x^{2} - 2 g o f = g (f (x)) = g (2 x + 1) = {(2 x + 1)}^{2} - 2 = 4 x^{2} + 1 + 4 x - 2 = 4 x^{2} + 4 x - 1 f o g = f (g (x)) = f (x^{2} - 2) = 2 (x^{2} - 2) + 1 = 2 x^{2} - 4 + 1 = 2 x^{2} - 3$

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