Question

Let f(x) = 1/π(sin^-1x + cos^-1x + tan^-1x) + (x + 1)/(x² + 2x + 10) such that the maximum value of f(x) is m, then find the value of(104m - 90).

Answer 1

We have

f(x) = 1/π(sin^-1x + cos^-1x + tan^-1x) + (x + 1)/(x² + 2x + 10)

It will provide us the max value at x = 1

f(x) = 1/π(π/2 + tan^-1(1)) + 2/13

= 1/π x 3π/4 + 2/13

= 3/4 + 2/13 = (39 + 8)/52 = 47/52

Hence, the value of (104m - 90) is 4.