Sketch the graphs of $y=\left| x \right|$ and $y=\frac{c}{x-c}$, where $c0$, on the same diagram, s

Question

Sketch the graphs of $y=\left| x \right|$ and $y=\frac{c}{x-c}$, where $c>0$, on the same diagram, stating clearly the coordinates of any points where the curves cross the axes. [2] Solve the equation $\left| x \right|=\frac{c}{x-c}$, leaving your answer in terms of $c$. [2] Hence solve the inequality $\left| x \right|>\frac{c}{\left| x \right|-c}.$ [1]

Accepted Answer

$x = (c + √(c² + 4c))/2; Inequality: x > (c + √(c² + 4c))/2 or x < -(c + √(c² + 4c))/2 or -c < x < c$

2020 ACJC Promo Q4

2020 ACJC Promo Q4

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