Question

Find the domain for which the functions $f\left(x\right)=2x^2-1$ and $g\left(x\right)=1-3x$ are equal.

• A. {-2,2}
• B. {2, 1/2}
• C. {-2,1/2}
• D. None of these

Answer 1

The correct option is C {-2,1/2}

The values of x for which f(x) and g(x) are equal are given by

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

$⟹2x^2-1=1-3x$

$2x^2+3x-2=0$

$(x+2)(2x-1)=0$

$x=-2,1/2$.

Thus, $f\left(x\right)$ and $g\left(x\right)$ are equal on the set {-2, 1/2}.