The function f is such that f(x)�

Question

= 2x + 3 for x ≥ 0.
The function g is such that g(x)�= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)�= 6x^2 − 21 for x ≤ q.
i)Find the values of a and b
ii) Find the greatest possible value of q.
It is now given that q = -3
iii) Find the range of fg
iv)Find the expression for inverse of (fg)(x) ad state the domain of the inverse of (fg)

Answer 1

fg = (2x+3)(ax^2+b) = 6x^2-21
2ax^3+3ax^2+bx+3b = 6x^2-21
when x=q, we have

2aq^3+3aq^2+bq+3b=6q^2-21
2aq^3+(3a-6)q^2+bq+(3b-21) = 0

check out the solutions to that at this url. The only easy one is in fact when q = -3.

http://www.wolframalpha.com/input/?i=2aq%5E3%2B(3a-6)q%5E2%2Bbq%2B(3b-21)+%3D+0

Answer 2

Thanks a lot Steve!!!