pr3tyana
contestada

if 0 < x < 1 , which of the following lists the numbers in increasing order ??
(a) √x , x , x²
(b) x² , x , √x
(c) x² , √x , x

Respuesta :

darth666
answer B

[tex]x = \frac{1}{4}[/tex]    
[tex]\sqrt{ \frac{1}{4} }= \frac{1}{2}[/tex] 
[tex](\frac{1}{4})^2 = \frac{1}{16}[/tex]

[tex] \frac{1}{16}\ \textless \ \frac{1}{4}\ \textless \ \frac{1}{2} [/tex]

Answer:

(b) x² , x , √x

Step-by-step explanation:

Since, when x is a real number,

Such that 0 < x < 1

Then with increasing the exponent of x the value of x decreases,

That is, x with highest exponent is lowest,

Since,

[tex]2 > 1 > \frac{1}{2}[/tex]

Thus, by the above statement,

[tex]x^2 < x < x^\frac{1}{2}[/tex]

Hence, the numbers in increasing order is,

x² , x , √x

Where, 0 < x < 1

Option (b) is correct.

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