If the mapping

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

If the mapping f(x)=ax+bf(x)=ax+b, where a<0a<0, maps [−1,1][-1,1] onto [0,2][0,2], then, for all values of θ\theta, A=cos⁡2θ+sin⁡4θA=\cos^2\theta+\sin^4\theta satisfies (1) f(14)≤A≤f(0)f\left(\frac14\right)\leq A\leq f(0) (2) f(0)≤A≤f(−2)f(0)\leq A\leq f(-2) (3) f(13)≤A≤f(0)f\left(\frac13\right)\leq A\leq f(0) (4) f(−1)<A≤f(−2)f(-1)<A\leq f(-2)

Related theory

Browse the problem library