Question

If the range of the function f(x) = x²/(x⁴ + 1) is [a, b/c], where a, b, c ∈ I then find the value of (a + b + c + 2)

Answer 1

Clearly, f(x) ≥ 0 for any x in R When x is non zero, 

f(x) = 1/(x² + 1/x²) ≤ 1/2)

But at x = 0, f(0) = 0

Thus, the range of the given function is [ 0, 1/2]

Clearly, a = 0, b = 1 and c = 2

Hence, the value of (a + b + c + 2) is 5