Question

If the value of x lies between 0 & 1 which of the following is the largest?

(a) x b) x2 (c) –x (d) 1/x

Answer 1

The required answer is 1/x

So option d is correct

Answer 2

Answer:

$\frac{1}{x}$

Step-by-step explanation:

If a number x lies between 0 & 1,

Then it is a perfect fraction,

i.e.

$x=\frac{a}{b}< 1$

Where, a < b

So, $\frac{1}{x}=\frac{b}{a}> \frac{a}{b} = x$ where, a < b,

Now,

if x is perfect fraction,

⇒ x² is also a perfect fraction,

i.e. $x^2 < 1$

And, $\frac{1}{x}>1$

$\implies \frac{1}{x}> x^2$

Hence, $\frac{1}{x}$ is largest for all x ∈ (0, 1)