Find the domain for which the function $f (x) = 3 x^{2} - 2 x$ and $g (x) = 9 x - 6$ are equal.

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Solution

Consider the given function.

$f (x) = 3 x^{2} - 2 x$

$g (x) = 9 x - 6$

If $f (x) = g (x)$ , then

$3 x^{2} - 2 x = 9 x - 6$

$3 x^{2} - 11 x + 6 = 0$

$3 x^{2} - 2 x - 9 x + 6 = 0$

$x (3 x - 2) - 3 (3 x - 2) = 0$

$(x - 3) (3 x - 2) = 0$

$x = \frac{2}{3}, 3$

Therefore,
Required domain $= {\frac{2}{3}, 3}$

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Find the set of values of x for which the functions $f (x) = 3 x^{2} - 1$ and $g (x) = 3 + x$ are equal.

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