Question

If sin^–1 x + sin^–1y + sin^–1z = $\frac{3\pi}{2}$and

f(1) = 2, f(p +q) = f(p). f(q) " p, q Î R, then

$x^{f(1)} + y^{f(2)} + z^{f(3)}$– $\frac{x + y + z}{x^{f(1)} + y^{f(2)} + z^{f(3)}}$=

• A. 0
• B. 1
• C. 2
• D.

Answer 1

Answer: (C)

2

Answer 2

– $\frac{\pi}{2}$£ sin^–1 x £ $\frac{\pi}{2}$

\ sin^–1 x + sin^–1 y + sin^{– 1}z = $\frac{3\pi}{2}$

Û sin^–1 x = sin^–1 y = sin^{– 1}z = $\frac{\pi}{2}$

Û x = y = z = 1

Also f(p + q) = f(p). f(q) " p, q Î R …(1)

Given f(1) = 1

from (1),

F(1 + 1) = f(1). F(1) ̃ f(2) =1² = 1

from (2), f(2 + 1) = f(2) . f(1)

̃ f(3) = 1². 1 = 1³ = 1

Now given expression = 3 – $\frac{3}{3}$= 2