Find the domain of the function f(x) = x^2 + 2x + 1 x^2 - 8x + 12… - Vidyadip

Question

Find the domain of the function $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$.

✓

Answer

Here $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$
f (x) is a rational function of x.
f (x) assumes real values of all x except for those values of x for which
$x^2-8 x+12=0$
$\Rightarrow(x-6)(x-2)=0$
$\Rightarrow x=2,6$
$\therefore$ Domain of function $=R-\{2,6\}$.

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 "(Each question 2 marks)" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove that: $\begin{equation} \frac{\sin 5 x-2 \sin 3 x+\sin x}{\cos 5 x-\cos x}=\tan x \end{equation}$

A bag contains 5 red, 6 white and 9 blue balls. two balls are dreawn at random. what is the probability that both balls are red or both are black?

In a single throw of a die describe the following events: F = Getting a number not less than 3. Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and F.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-4^\text{x}-2^\text{x}+1}{\text{x}^2}$

Evaluate the following: $\text{i}^{30}+\text{i}^{40}+\text{i}^{60}$

Prove that: $\cos 4 x=1-8 \sin ^2 x \cos ^2 x$

Find the modulus of $\frac{{1 + i}}{{1 - i}} - \frac{{1 - i}}{{1 + i}}$.

Write the sets $\Big\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\Big\}$ in the set-builder form.

Find the sum of the following geometric series: $\text{x}^3,\text{x}^5,\text{x}^7,\ ...\ \text{to n terms}$

Differentiate the following function with respect to x:$\text{x}^5\text{e}^\text{x}+\text{x}^6\log\text{x}$