Question

find the set of valuesfor which the functionf (x)=1-3x and g (x)=2x2-1 are equal

Answer 1

Ans.

Given that
f(x) = 1 - 3x
$g(x) = 2 {x}^{2} - 1$
If f(x) and g(x) are equal, then -
$1 - 3x = 2 {x}^{2} - 1 \\ or \: \: 2 {x}^{2} + 3x - 2 = 0 \\ or \: \: 2 {x}^{2} + 4x - x - 2 = 0 \\ or \: \: 2x(x + 2) - (x + 2) = 0 \\ or \: \: (x + 2)(2x - 1) = 0$
Therefore,
$x = - 2 \: \: or \: \: x = \frac{1}{2}$

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