If a polynomial function `f(x)` satisfies `f(f(f(x))=8x+21 ,` where `p` and `q` are real numbers, then `p+q` is equal to _______

Answer

5

Explanation

`f(x)` must be linear function. Therefore,
`f(x)=px+q`
` :. f(f(x))=pf(x)+q=p(px+q)+q=p^(2)x+pq+q`
` :. f(f(f(x)))=p(p^(2)x+pq+q)+q`
` =p^(3)x+p^(2)q+pq+q`
`=8x+21 ` (Given)
` :. P^(3)=8 or p=2`
and `p^(2)q +pq+q=21 or q=3`
` :. p+q=5`