Question

The domain for which the functions defined by $f\left(x\right)=3x^2–1$ and $g\left(x\right)=3+x$ are equal is

• A. $\{-1,\frac{4}{3}\}$
• B. $(-1,\frac{4}{3})$
• C. $(-1,\frac{4}{3}]$
• D. $[-1,\frac{4}{3}]$

Answer 1

The correct option is A $\{-1,\frac{4}{3}\}$

Given:$f\left(x\right)=3x^2–1$ and $g\left(x\right)=3+x$

Also,$f\left(x\right)=g\left(x\right)$

$\Rightarrow 3x^2–1=3+x$

$\Rightarrow 3x^2–x–4=0$

$\Rightarrow 3x^2–4x+3x–4=0$

$\Rightarrow 3x(x+1)-4(x+1)=0$

$\Rightarrow (x+1)(3x-4)=0$

$\Rightarrow x=-1,\frac{4}{3}$

$\therefore$Domain $=-1,\frac{4}{3}$