I Find the domain of the function fx-x2-2 x-1-x2-8 x-12-ii Let A -8-11-15-12-15-18-23 and f be function from A - N- such that f x is the highest prime factor of x- Find f and its range-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Arrhenius Acid

i Find the do...

Question

(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.

Open in App

Solution

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

Since, f(x) is a rational function of x.

Hence, f(x) assumes real value of x except for those values of x for which $x^{2} - 8 x + 12 = 0.$

$\Rightarrow x^{2} - 8 x + 12 = 0 \Rightarrow (x - 6) (x - 2) = 0 \Rightarrow x = 2 a n d 6$

$∴$ Domain of function = $R - {2, 6}$

(ii) Given, $A = {8, 11, 15, 12, 18, 23}$ and f is a function from $A \to N$ such that

f(x) = Highest prime factor of x

$∴$ f(8) = Highest prime factor of 8 = 2

f(11) = Highest prime factor of 11 = 11

f(12) = Highest prime factor of 12 = 3

f(15) = Highest prime factor of 15 = 5

f(18) = Highest prime factor of 18 = 3

f(23) = Highest prime factor of 23 = 23

$f = {(8, 2), (11, 11), (12, 3), (15, 5), (18, 3), (23, 23)}$

Hence, range of f is ${2, 11, 3, 5, 23}$

Suggest Corrections

Similar questions

Let $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real functions. Find (f + g), (f - g) (x), (fg) (x) and $(\frac{f}{g}) (x)$

Q. Let A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.

Q. Find the domain of the function

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

Q. Find the domain and range of the following real functions:
i)

f (x) = - | x |

ii)

f (x) = \sqrt{9 - x^{2}}

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

Join BYJU'S Learning Program

(i) Find the domain of the function f(x)=x2+2x+1x2−8x+12. (ii) Let A={8,11,15,12,15,18,23} and f be function from A→N, such that f(x) is the highest prime factor of x. Find f and its range.

(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.