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

The given function is, #160; f(x) = x^2+2x+1/x^2 8x+12 ⇒f(x) =x^2+2x+1/ ( x 6 ) ( x 2 ) It can be seen that function f is defined for all re ...

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Standard XII

Mathematics

Existence of Limit

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

The given function is, $f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}$
$\Rightarrow f (x) = \frac{x^{2} + 2 x + 1}{(x - 6) (x - 2)}$

It can be seen that function $f$ is defined for all real numbers except at $x = 6$ and $x = 2$
Hence the domain of $f$ 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) $f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}$

Find the domain of the function:

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

Q. The range of the function

f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}

Q. 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}

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

(ii) Let $A = {8, 11, 15, 12, 15, 18, 23}$ and f be function from $A \to N,$ such that f(x) is the highest prime factor of x. Find f and its range.

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Find the domain of the function f(x)=x2+2x+1x2−8x+12

The given function is, f(x)=x2+2x+1x2−8x+12⇒f(x)=x2+2x+1(x−6)(x−2)It can be seen that function f is defined for all real numbers except at x=6 and x=2 Hence the domain of f is R−{2,6}

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

The given function is, $f (x) = \frac{x^{2} + 2 x + 1}{x^{2} - 8 x + 12}$
$\Rightarrow f (x) = \frac{x^{2} + 2 x + 1}{(x - 6) (x - 2)}$

It can be seen that function $f$ is defined for all real numbers except at $x = 6$ and $x = 2$
Hence the domain of $f$ is $R - {2, 6}$