If \(f(x) = {\sin ^{ - 1}}\left[ {\frac{{\sqrt 3 }}{2}x - \frac{1}{2}\sqrt {1 - {x^2}} } \right]\), \(x \in \left[ { - \frac{1}{2},1} \right]\), then f(x) will be

\({\sin ^{ - 1}}\left( {x - \frac{\pi }{4}} \right)\)

\({\sin ^{ - 1}}\left( {x - \frac{\pi }{2}} \right)\)

\({\sin ^{ - 1}}\left( {x - \frac{\pi }{3}} \right)\)

\({\sin ^{ - 1}}x ~-\frac{\pi}{6}\)

If \(f(x) = {\sin ^{ - 1}}\left[ {\frac{{\sqrt 3 }}{2}x - \frac{1}{2}

1.	If \(f(x) = {\sin ^{ - 1}}\left[ {\frac{{\sqrt 3 }}{2}x - \frac{1}{2}\sqrt {1 - {x^2}} } \right]\), \(x \in \left[ { - \frac{1}{2},1} \right]\), then f(x) will be
A.	\({\sin ^{ - 1}}\left( {x - \frac{\pi }{2}} \right)\)
B.	\({\sin ^{ - 1}}\left( {x - \frac{\pi }{3}} \right)\)
C.	\({\sin ^{ - 1}}x ~-\frac{\pi}{6}\)
D.	\({\sin ^{ - 1}}\left( {x - \frac{\pi }{4}} \right)\)
Answer» D. \({\sin ^{ - 1}}\left( {x - \frac{\pi }{4}} \right)\)

If f(x) = x and g (x) = |x| then f o g (- 3.5) ?
If the number 235 in decimal system is converted into binary system, then what is the resulting number?
For x > 1, if (2x)2y = 4e(2x-2y), then \({\left( {1 + lo{g_e}2x} \right)^2}\frac{{dy}}{{dx}}\) is equal to
If x is any real number, then \(\frac{{{{\rm{x}}^2}}}{{1 + {{\rm{x}}^4}}}\) belongs to which one of the following intervals?
If \({\rm{f}}\left( {{{\rm{x}}_1}} \right) - {\rm{f}}\left( {{{\rm{x}}_2}} \right) = {\rm{f}}\left( {\frac{{{{\rm{x}}_1} - {{\rm{x}}_2}}}{{1 - {{\rm{x}}_1}{{\rm{x}}_2}}}} \right)\) for x1, x2 ∈ (-1, 1), then what is f(x) equal to?
Let A = {x ∈ R : x is not a positive integer}. Define a function \(f:A \to R{\rm{\;as\;}}f\left( x \right) = \frac{{2x}}{{x - 1}}\) then f is:
If \(f\left( x \right) = \frac{{x - 2}}{{x + 2}},\;x \ne - 2\), then what is f-1(x) equal to?
If log102 = 0.3010 and log103 = 0.4771, then the value of log100 (0.72) is equal to
If E is the universal set and A = B ∪ C, then the set E - (E - (E - (E - (E - A)))) is same as the set
Let f be a differentiable function such that f(1) = 2 and f(x) = f(x) for all x ∈ R If h(x) = f(f(x)), then h' (1) is equal to