Let g: R arrow[(π/6), (π/2)) is defined by g(x)= sin -1((x2-c/1+x2)). Then the possible values of ' c ' for which g is surjective function, is

Question

Let g: R arrow[(π/6), (π/2)) is defined by g(x)= sin -1((x2-c/1+x2)). Then the possible values of ' c ' for which g is surjective function, is (A)  (1/2)  (B) (-1,-(1/2)] (C)  -(1/2)  (D) (-(1/2), 1]

Tardigrade Admin · Accepted Answer

Correct answer is (b) (-1,-(1/2)]

Q. Let $g : R \to [\frac{π}{6}, \frac{π}{2})$ is defined by $g (x) = sin^{- 1} (\frac{x ^{2} - c}{1 + x ^{2}})$ . Then the possible values of ' $c$ ' for which $g$ is surjective function, is

${\frac{1}{2}}$

$(- 1, - \frac{1}{2}]$

${- \frac{1}{2}}$

$(- \frac{1}{2}, 1]$

Correct answer is (b) $(- 1, - \frac{1}{2}]$

Q. Let g:R→[6π​,2π​) is defined by g(x)=sin−1(1+x2x2−c​). Then the possible values of ' c ' for which g is surjective function, is

{21​}

(−1,−21​]

{−21​}

(−21​,1]