Question:
if f;R....R and g : R....R defined respectively as f(x) =x^2 =3x 1 and g(x) =2x-3 .find fog and gof
Answer:
Given, f(x) = x2 - 3x + 1
and g(x) = 2x - 3
1. fog(x) = f(g(x))
= f(2x - 3)
= (2x - 3)2 - 3(2x - 3) + 1
= 4x2 - 2*2x*3 + 9 - 6x + 9 + 1
= 4x2 - 12x + 9 - 6x + 9 + 1
= 4x2 - 18x + 19
=> fog(x) = 4x2 - 18x + 19
2. gof(x) = g(f(x))
= g(x2 - 3x + 1)
= 2(x2 - 3x + 1) - 3
= 2x2 - 6x + 2 - 3
= 2x2 - 6x - 1
=> gof(x) = 2x2 - 6x - 1
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