The-domaine-of-the-function-f-x-log-0-5-x-2-7x-13-1-is-

Question Number 121278 by Ar Brandon last updated on 06/Nov/20

The domaine of the function

f (x) = {(\sqrt{\log_{0.5} (x^{2} - 7 x + 13)})}^{- 1} is;

Answered by TANMAY PANACEA last updated on 06/Nov/20

x^{2} - 7 x + 13

(x^{2} - 2 \times x \times \frac{7}{2} + \frac{49}{4} + 13 - \frac{49}{4})

{(x - \frac{7}{2})}^{2} + \frac{3}{4} > 0

s o g (x) = x^{2} - 7 x + 13 > 0

f (x) = \frac{1}{\sqrt{{l o g}_{0.5} (x^{2} - 7 x + 13)}}

n o t e (x^{2} - 7 x + 13) c a n n o t b e e q u s l s t o 1

i f x^{2} - 7 x + 13 = 1

f (x) = \frac{1}{\sqrt{{l o g}_{0.5} 1}} = \frac{1}{0} = u n d d f i n e d

s o 1 > (x^{2} - 7 x + 13) > 0

x^{2} - 7 x + 13 < 1

x^{2} - 7 x + 12 < 0

(x - 3) (x - 4) < 0

w h e n x > 4 (x - 3) (x - 4) > 0 n o t f e a s i b l d

w h e n x < 3 (x - 3) (x - 4) > 0 n o t f e a s i b l e

w h e n 4 > x > 3 (x - 3) (x - 4) < 0 f e a s i b l e

s o d o m a i n \dots 4 > x > 3

Commented by TANMAY PANACEA last updated on 06/Nov/20

Commented by Ar Brandon last updated on 06/Nov/20

Thanks Sir

Commented by TANMAY PANACEA last updated on 06/Nov/20

m o s t s e l c o m e s i r