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If f: R → R is defined by f(x) = ax + 3 and g: R → R is defined by g(x) = 4x – 3 find a so that fog = gof |
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Answer» f(x) = ax + 3 ; g(x) = 4x -3 fog = f[g(x)] = f(4x – 3) = a(4x – 3) + 3 = 4ax – 3a + 3 gof = g[f(x)] = g(ax + 3) = 4(ax + 3) – 3 = 4 ax + 12 – 3 = 4ax + 9 But fog = gof 4ax – 3a + 3 = 4ax + 9 -3a + 3 = 9 – 3a = 6 a = – 2 The value of a = – 2 |
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