Question

Write the range of the function f (x) = e^x-[x] ,x€R
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Answer 1

Answer:

Range of y is [2,∞)

Step-by-step explanation:

Let, y = e^x + e^(-x)

=> ye^x = e^(2x) + 1

=> e^(2x) -ye^x +1 = 0 …(1)

(1) is a quadratic equation in (e^x). Now, we know, for all real x, (e^x) is positive and real.

Therefore, discriminant of (1) must be non-negative.

i.e., (-y)^2 -4×1×1 ≥ 0

=> y^2 ≥ 4

=> y ≥ 2 [Since, y > 0.]

Therefore, range of y is [2,∞).