Find the domain of the function fx-x2-2x-1x2-8x-12-

Step 1: Given f(x)=x^2+2x+1x^2 8x+12. Step 2: Domain of function f(x)=(x+1)^2x^2 6x 2x+12. f(x)= (x+1)^2x(x 6) 2(x 6) f(x) = (x+1)^2(x 2)(x 6) It can be see ...

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Byju's Answer

Standard X

Mathematics

Discriminant

Find the doma...

Question

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

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Solution

Step 1: Given $f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}$ .

Step 2: Domain of function
$f (x) = \frac{(x + 1)^{2}}{x^{2} - 6 x - 2 x + 12}$ .

$f (x) = \frac{(x + 1)^{2}}{x (x - 6) - 2 (x - 6)}$

$f (x) = \frac{(x + 1)^{2}}{(x - 2) (x - 6)}$

It can be seen that the function f is defined for all real numbers except at x=6 and x=2.

Hence, the domain of the function is R - {2, 6}.

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Similar questions

Find the domain of each of the following real valued functions of real variable :
(i) $f (x) = \frac{1}{x}$
(ii) $f (x) = \frac{1}{x - 7}$
(iii) $f (x) = \frac{3 x - 2}{x + 1}$
(iv) $f (x) = \frac{2 x + 1}{x^{2} - 9}$
(v) $f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}$