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An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b₁, b₂, b₃} and G = {g₁, g₂}, where B represents the set of Boys selected and G the set of Girls selected for the final race.
Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y ∈ N}. What is the domain, codomain and range of R? Is this relation a function?
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x).
The relation f is defined by f(x) = x², 0 ≤ x ≤ 3 and 3x, 3 ≤ x ≤ 10. The relation g is defined by g(x) = x², 0 ≤ x ≤ 2 and 3x, 2 ≤ x ≤ 10. Show that f is a function and g is not a function.
Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
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