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Let f: R → R: f(x) = (x2 + 3x + 1) and g: R → R: g(x) = (2x – 3). Write down the formulae for

(i) g o f (ii) f o g (iii) g o g.

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It is given that

f(x) = (x2 + 3x + 1) and g(x) = (2x – 3)

(i) g o f = g o f (x) = g{f(x)} = g(x2 + 3x + 1)

So we get

= 2 (x2 + 3x + 1) – 3

It can be written as

= 2x2 + 6x + 2 – 3

On further calculation

= 2x2 + 6x – 1

(ii) f o g = f o g (x) = f{g(x)} = f {2x – 3}

So we get

= (2x – 3)2 + 3 (2x – 3) + 1

It can be written as

= 4x2 – 12x + 9 + 6x – 9 + 1

On further calculation

= 4x2 – 6x + 1

(iii) g o g = g o g (x) = g {g(x)} = g{2x – 3}

So we get

= 2 (2x – 3) – 3

It can be written as

= 4x – 6 – 3

On further calculation

= 4x – 9

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