Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Set of Values of X for Which the Functions F(X) = 3x2 − 1 and G(X) = 3 + X Are Equal. - Mathematics

Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.

#### Solution

It is given that the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.

$\therefore f\left( x \right) = g\left( x \right)$
$\Rightarrow 3 x^2 - 1 = 3 + x$
$\Rightarrow 3 x^2 - x - 4 = 0$
$\Rightarrow \left( x + 1 \right)\left( 3x - 4 \right) = 0$

$\Rightarrow x + 1 = 0 \text{ or } 3x - 4 = 0$
$\Rightarrow x = - 1 \text{ or } x = \frac{4}{3}$

Hence, the set of values of x for which the given functions are equal is $\left\{ - 1, \frac{4}{3} \right\}$ .

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.5 | Q 17 | Page 42