Note: if you see symbols like ³ or Þ in various places, then the Symbol or WP MathA font is not installed on your computer. The translation is:
- = - (minus) | Þ = Þ (implies) |
¥ = ¥ (infinity) | Ö = Ö (check mark) |
Check for division by zero:
2 - x = 0 at
x = 2.
The left hand side = 0 at x = 1
The test intervals are
(-¥, 1], [1, 2) and
(2, ¥).
(-¥, 1] :
Try x = 0 :
Ö
[1, 2) :
Try x = 3/2 :
×
(2, ¥) :
Try x = 3 :
Ö
Therefore the solution set is
Alternative method:
[The same up to]
Þ
(x > 1 AND x > 2) OR
(x < 1 AND x < 2)
Þ
x > 2 OR x < 1
Þ
(-¥, 1] |
---|
f -1(x) = 1 - x2 |
---|
(-¥, 0] |
---|
[Note that if the domain of the inverse function were extended
to the full default domain of
It is easier to sketch the inverse function first, as it is the
left half of a parabola,
opening downwards, with y-intercept = 1 and
x-intercepts = ±1.
The graph of f (x) is then its
reflection in the line y = x.
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