f(x) = 3[x] - 1 and g(x) = {3x – 2} + 4, where [x] is the greatest integer less than or equal to x and {x} is the fractional part of x. Find f(x) + g(x) for all integer values of x.
Explanation:
f(x) = 3[x] - 1
As x is an integer, [x] = x
∴ f(x) = 3[x] - 1 = 3x - 1 Also, g(x) = {3x – 2} + 4 Since x is an integer, (3x – 2) is also an integer. ∴ Fractional part of (3x – 2) = 0 ∴ f(x) + g(x) = 3x - 1 + 4 = 3x + 3 Hence, option (b).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.