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+1 vote
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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

1 Answer

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Best 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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