Find the domain and range of the function f(x)=x^2-9 x-3 - Vidyadip

Question

Find the domain and range of the function $f(x)=\frac{x^2-9}{x-3}$

✓

Answer

Here $f(x)=\frac{x^2-9}{x-3}$
$f(x)$ assume real values for all real values of $x$ except for $x - 3 = 0$
i.e $x = 3$
Thus domain of $f (x) = R - {3}$
Let $f (x) = y$
$\therefore y=\frac{x^2-9}{x-3}$
$=\frac{(x+3)(x-3)}{(x-3)}$
$\Rightarrow y=x+3$
$y$ takes all real values except $6$ as domain $=R-{3}$
Thus range of $f(x) = R - {6}.$

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 "3 Marks Question" from Model Paper 1→Model Paper 1 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The sum of three numbers in $G.P.$ is $14.$ If the first two terms are each increased by $1$ and the third term decreased by $1,$ the resulting numbers are in $A.P.$ Find the numbers.

Find the sum to indicated number of terms of the geometric progression $ \sqrt { 7 } , \sqrt { 21 } , 3 \sqrt { 7 }$, ... n terms.

Differentiate the following function with respect to x:$\text{x}^{-3}(5+\text{3x})$

In how many ways can a football team of $11$ players be selected from $16$ players? How many of them will.

Include $2$ particular players?
Exclude $2$ particular players?

Find the mean and standard deviation of the age distribution given in the following table of 542 persons :

Age (In years)	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90
Number of Persons	3	61	132	153	140	51	2

Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science, $4$ in English and Science, $4$ in all the three. Find how many passed
$i.$ in English and Mathematics but not in Science
$ii$. in Mathematics and Science but not in English
$iii.$ in Mathematics only
$iv$. in more than one subject only

If the $AM$ and $GM$ of two positive numbers $a$ and $b$ are in the ratio $m : n$, show that $a : b =\left(m+\sqrt{m^2-n^2}\right):\left(m-\sqrt{m^2-n^2}\right)$

Find $(a + b)^4 - (a - b)^4.$ Hence, evaluate ${(\sqrt 3 + \sqrt 2 )^4} - {(\sqrt 3 - \sqrt 2 )^4}$

Evaluate the following:
$^{n+1}C_n$

Find the length of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).