(a)[2]
Find the greatest value of $a$ for which the composite function $fg$ can be formed.
(b)[3]
When $a = -1$, solve $fg(x) + 14 = 0$.
(c)[4]
When $a = -1$, find all values of $x$ that satisfy $fg(x) \leq -50$.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The rule for $f$ is $f(x) = 3x + 1$ when $x \leq a$, where $a$ is constant. The rule for $g$ is $g(x) = -1 - x^2$ when $x \leq -1$.