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19 March, 10:28

f (x) = ax + b and g (x) = x-4, where a and b are constant. If fg (4) = 2 and gf (2) = 4, find the values of a and b.

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  1. 19 March, 12:15
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    Answer: a = 3, b = 2

    Step-by-step explanation:

    f (x) = ax + b f (2) = 2a + b

    g (x) = x - 4 g (4) = 4 - 4 ⇒ g (4) = 0

    f (g (4)) = 2 ⇒ f (0) = 2

    and f (0) = a (0) + b ⇒ f (0) = b

    ⇒ 2 = b

    g (f (2)) = 4 ⇒ g (2a+b) = 4

    and g (2a + b) = (2a + b) - 4 ⇒ g (2a + 2) = 2a + 2 - 4 ⇒ g (2a + 2) = 2a - 2

    ⇒ 4 = 2a - 2

    6 = 2a

    3 = a
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