Question

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:

Accepted Answer

C. $f(f(x)) = a(ax + b) + b = a^2 x + ab + b$. Given $f(f(x)) = 9x + 8$, we equate coefficients: $a^2 = 9 \implies a = 3$ (since $a$ is positive). $ab + b = 8 \implies 3b + b = 8 \implies 4b = 8 \implies b = 2$. Hence, $a + b = 3 + 2 = 5$.

Composite Linear Function Coefficients

Explanation

Practise this under exam conditions