Question

Let $f\left(x\right)=x^2-12x-10.$ Then

• A. domain of $f$ is $R$
• B. domain of $f$ is $R-\left\{6\right\}$
• C. range of $f$ is $R$
• D. range of $f$ is $[-46,\infty )$

Answer 1

Answer: (A), (D)

The correct options are
A domain of $f$ is $R$
D range of $f$ is $[-46,\infty )$

$f\left(x\right)=x^2-12x-10$
$\Rightarrow f\left(x\right)=(x-6{)}^2-46$
Clearly, $f$ is defined for all real values of $x$
Hence, domain $=R$

$0\le (x-6{)}^2<\infty$
$\Rightarrow -46\le (x-6{)}^2-46<\infty$
Hence, range of $f$ is $[-46,\infty )$