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Given f(x) = 3x – 2; g(x) = 2x^2 find (i) fog and (ii) gof what do you find

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Given f(x) = 3x – 2; g(x) = 2x2 find

(i) fog and

(ii) gof what do you find

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f(x) = 3x – 2 ; g(x) = 2x2

(i) fog = f[g(x)]

= f(2x2)

= 3(2x2) – 2

= 6x2 – 2

(ii) gof = g[f(x)]

= g(3x – 2)

= 2(3x – 2)2

= 2(9x2 + 4 – 12x)

= 18x2 – 24x + 8

We find that fog ≠ gof

Composition of function is not commutative.

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