Consider the relation f defined by f(x) = \\begin{array}{c}{x^2\\\\\\end{array},0\leqx\leq3;{3x;},3\leqx\leq10 and the relation g defined by , g(x) = \\begin{array}{c}{x^2\\\\\\end{array},0\leqx\leq2;{3x;},2\leqx\leq10 , then

Correct Answer is : f is a function but g is not

HCU MCA 2013 Paper

Question : 37 of 75

Marks: +1, -0

Consider the relation f defined by
f(x) =

\{\table {x^2\;;},0≤x≤3;{3x;},3≤x≤10

and the relation g defined by ,
g(x) =

\{\table {x^2\;;},0≤x≤2;{3x;},2≤x≤10

, then

Solution:

\{\table {x^2\;;},0≤x≤3;{3x;},3≤x≤10

and g(x) =

\{\table {x^2\;;},0≤x≤2;{3x;},2≤x≤10

(i)

Hence, it is a continuous function.
(ii)

Hence, we see that at x = 2, we get two different values of y. So g(x) is not a function,

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