QUESTION 6
The graphs of $f(x) = ax^2$ and $g(x) = bx$ are sketched on the same set of axes. Points
A(-1;2) and B are points of intersection of $f$ and $g$. The graph of $f$ has the turning
point at the origin:
y
A(-1;2)
B
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6.1 Calculate the values of $a$ and $b$.
(2)
6.2 The inverse of $f$ is NOT a function. Write down at least one condition which
can be used to restrict the domain of $f$ such that its inverse will be a function. (1)
6.3 For which value(s) of $x$, where $x \in (-\infty; 0)$, will $g(x) \le f(x)$?
(2)
6.4 If $h(x) = g(x+3)$, write down the coordinates of
6.4.1 A', the new coordinates of A on the graph of $h$.
(1)
6.4.2 A", the new coordinates of A on the graph of $h^{-1}$, the inverse of $h$ (2)
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