Please solve it in wavy curve method Illustration 3: Find the set of all x for which 1x-13-x≤1 - Maths - Relations and Functions

Question

Please solve it in wavy curve method
Illustration 3: Find the set of all x for which 1 x - 1 3 - x
≤ 1

Aarushi Mishra · Accepted Answer

1x-13-x≤1For applying wavy curve method, the coefficient of x should be positive-1x-1x-3≤11+1x-1x-3≥0x-1x-3+1x-1x-3≥0x2-4x+3+1x-1x-3≥0x2-4x+4x-1x-3≥0x-22x-1x-3≥0Clearly critical points are: 1,2 and 3

<img alt="" src=
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style="width: 501px; height: 154px;">
x∈-∞,1∪3,∞∪2We need to included 2 because at x=2 the expression is zero

Please solve it in wavy curve method. Illustration 3: Find the set of all x for which 1 x - 1 3 - x ≤ 1 .

Please solve it in wavy curve method.
Illustration 3: Find the set of all x for which $\frac{1}{(x - 1) (3 - x)} \leq 1$ .