Question
Download Solution PDFIf f(y) = (y)[y] where [.] denotes smallest integer function and g(y) = y2 then find the value of g o f(- 3/2) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Smallest integer function:
The function f (x) = [x] is called the smallest integer function and it means that the smallest integer is greater than or equal to x i.e [x] ≥ x.
The graph for the smallest integer function is given below,
Calculation:
Given: f(y) = (y)[y] where [.] denotes smallest integer function and g(y) = y2
Here, we have to find the value of g o f(- 3/2)
⇒ g o f(- 3/2) = g( f(- 3/2))
∵ f(y) = (y)[y] where [.] denotes the smallest integer function
⇒ f(- 3/2) = (-3/2)[- 3/2]
As we know that, [- 3/2] = - 1
⇒ f(- 3/2) = (- 3/2)-1 = - 2/3
⇒ g o f(- 3/2) = g(-2/3)
∵ g(y) = y2 so, g(-2/3) = (-2/3)2 = 4/9
Hence, g o f(- 3/2) = 4/9
Last updated on Jul 4, 2025
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