If the mapping ,

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If the mapping f(x)=mx+cf(x)=mx+c, m>0m>0, maps [−1,1][-1,1] onto [0,2][0,2], then tan⁡(tan⁡−117+cot⁡−18+cot⁡−118)\tan\left(\tan^{-1}\frac{1}{7}+\cot^{-1}8+\cot^{-1}18\right) is equal to (1) f(23)f\left(\frac{2}{3}\right) (2) f(13)f\left(\frac{1}{3}\right) (3) f(−13)f\left(-\frac{1}{3}\right) (4) f(−23)f\left(-\frac{2}{3}\right)

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