The-range-of-f-x-10-x-10-4-10-x-10-2-is-

Question Number 15086 by Tinkutara last updated on 07/Jun/17

The range of f (x) = \sqrt{\frac{10^{x} - 10^{4}}{10^{x} + 10^{2}}} is ?

Answered by ajfour last updated on 07/Jun/17

f (x) = \sqrt{1 - (\frac{10^{4} + 10^{2}}{10^{x} + 10^{2}})}

\Rightarrow x ⩾ 4

f o r x < 4, f (x) i s n o t r e a l

a t x = 4, f (x) = 0

a s x i n c r e a s e s f (x) i n c r e a s e s

f o r x \to \infty, f (x) \to 1

t h e r e f o r e, r a n g e o f f (x) i s

[0, 1) .

Commented by Tinkutara last updated on 07/Jun/17

Thanks Sir!