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Given f(x) = 5x + 2; g(x) = 2x – 3; h(x) = 3x + 1. Verify fo(goh) = (fog)oh |
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Answer» f(x) = 5x + 2; g(x) = 2x – 3; h(x) = 3x + 1 L.H.S. = fo(goh) goh = g[h(x)] = g(3x + 1) = 2(3x + 1) – 3 = 6x – 1 fo(goh) = f[goh(x)] = f(6x – 1) = 5(6x – 1) + 2 = 30 x – 5 + 2 fo(goh) = 30x – 3 … (1) R.H.S. = (fog)oh fog = f[g(x)] = f(2x – 3) = 5(2x – 3) + 2 = 30x – 5 + 2 fo(goh) = 30x – 3 …..(1) R.H.S. = (fog) oh fog = f[g(x)] = f(2x – 3) = 5 (2x – 3) = 5 (2x – 3) + 2 = 10x – 15 + 2 = 10x – 13 (fog) oh = fog [h(x)] = fog (3x + 1) = 10 (3x + 1) – 13 = 30x + 10 – 13 = 30x – 3 … (2) From (1) and (2) we get L.H.S. = R.H.S. fo(goh) = (fog)oh |
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