Question

If f(x) = sin^-1x + tan^-1x + x² + 4x + 5 such that R_f = [a, b], find the value of a + b + 5.

Answer 1

The domain of sin^-1x + tan^-1x is [-1, 1]

Now, f(1) = sin^-1(1)tan^-1(1) + 1 + 4 + 5

= 3π/4 + 10

and f(-1) = sin^-1(-1) + tan^-1(-1) + 1 - 4 + 5

= - 3π/4 + 2

Therefore, a + b + 5 = 10 + 2 + 5 = 17.