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If f(x) = ax + b and f( f(x)) = 8x + 21 where a, b  R, then find the value of (a + b + 3).

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Best answer

Given f(x) = ax + b

We have f( f(x))

= f(ax + b)

= a(ax + b) + b

= a2x + (ab + b) 

 Also, f(f(f(x))) 

= f(a2x + (ab + b)) 

= a(a2x + (ab + b)) + b 

= a3x + a(ab + ) + b 

= a3x + a2b + ab + b 

= 8x + 21 

Clearly, a = 2, b = 3

Hence, the value of (a + b + 3) is 8.

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