f-x-1-1-x-1-1-1-x-f-x-min-

Question Number 161590 by geron last updated on 20/Dec/21

f (x) = \frac{1}{1 - \sqrt{x}} + \frac{1}{1 - \sqrt{1 - x}}

f {(x)}_{m i n} = ?

Answered by cortano last updated on 20/Dec/21

Answered by mr W last updated on 20/Dec/21

0 < x < 1

l e t x = \sin^{2} (45 ° + θ) w i t h - 45 ° < θ < 45 °

f (x) = \frac{1}{1 - \sin (45 ° + θ)} + \frac{1}{1 - \cos (45 ° + θ)}

= \frac{1}{1 - \sin (45 ° + θ)} + \frac{1}{1 - \sin (45 ° - θ)}

f {(x)}_{m i n} = 2 \times \frac{1}{1 - \frac{1}{\sqrt{2}}} = 2 (2 + \sqrt{2})

a t θ = 0 ° o r x = \frac{1}{2}

Facebook Tweet Pin