Question

Find the range of $\frac{1}{\sqrt{x^2+5x+6}}$

• A. R
• B. ( 0 , )
• C. ( -3 , -2 )
• D. ( 3 , 2 )

Answer 1

The correct option is B

( 0 , )

$x^2$ + 5x + 6 is a quadratic expression, whose roots are -2 and -3. The graph of it will look like

It produces all the values from min (from the figure) to + $\infty$ .

$\Rightarrow$ All the values between zero and + $\infty$ are covered (because min is less than zero). $\sqrt{x^2+5x+6}$ won't be negative.

( $\sqrt{x}$ will always be greater than or equal to zero). , $\frac{1}{\sqrt{x^2+5x+6}}$ will take all the values between 0 and infinity.

[zero when $x^2$ + 5x + 6 tends to $\infty$ and $\infty$ when $x^2$ + 5x + 6 tends zero] .