Question

If f(x) = sin^–1$\sqrt{\frac{2}{5}}$, then f(x) is differentiable on

• A. [–1, 1]
• B. R – {–1,1}
• C. R – (–1, 1)
• D. None

Answer 1

Answer: (B)

R – {–1,1}

Answer 2

f ′(x) = $\frac { 1 } { \sqrt { 1 - \left( \frac { 2 x } { 1 + x ^ { 2 } } \right) ^ { 2 } } }$ ×

not defined when

1 – $\left( \frac { 2 x } { 1 + x ^ { 2 } } \right) ^ { 2 }$ = 0

(1 + x²)² – 4x² = 0 ⇒ (1 –x²)² = 0

x² = 1 x = 1, –1