Find the range of the following function : f(x)=x 9+x^2 - Vidyadip

Question

Find the range of the following function : $f(x)=\frac{x}{9+x^2}$

✓

Answer

$f(x)=\frac{x}{9+x^2}=y$ (say)
$\therefore \mathrm{x}^2 \mathrm{y}-\mathrm{x}+9 \mathrm{y}=0$
For real $x$, Discriminant $>0$
$ \therefore 1-4(y)(9 y) \geq 0$
$\therefore y^2 \leq \frac{1}{36}$
$\therefore \frac{-1}{6} \leq y \leq \frac{1}{6}$
$\therefore \text { Range of } f=\left[\frac{-1}{6}, \frac{1}{6}\right] $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Functions→Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the sum of $n$ terms of an $A.P.,$ is $3n^2 + 5n$ then which of its terms is $164$?

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{1+(\text{x}-1)^2}{1+{\text{x}^2}}$

State, first three terms in the expansion of $(5+4 x)^{-1 / 2}$

Which of the following relations are functions? If it is a function determine its domain and range.

{(2, 1), (3, 1), (5, 2)}

A die is thrown, find the probability of getting:
A prime number.

Write the sum of the series $1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ..... + (2n - 1)^2 - (2n)^2$

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed.

Write the domain and range of function f(x) given by $\text{f(x)}=\frac{1}{\sqrt{\text{x}-|\text{x}|}}$

Write the component statements of the following compound statements and check whether the compound statement is true or false:
All rational numbers are real and all real numbers are not complex.

In a simultanepous throw of a pair of dice, find the probability of getting:A doublet.