Let f: R → R: f(x) = (x2 + 3x + 1) and g: R → R: g(x) = (2x – 3

1.	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.
Answer» 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

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.

Answer»

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