If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:
Explanation:
f(x) = ax + b
∴ f(f(x) = a(ax + b) + b
f(f(x) = a2x + ab + b
⇒ a2x + b(a + 1) = 9x + 8
∴ a2 = 9 ⇒ a = 3. and
b(a + 1) = 8
⇒ b(3 + 1) = 8
⇒ b = 2
Thus, a + b = 5
Hence, option (c).
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