    Question

# Let g(x)=1x2,x>0;g(0)=0

A
g is a continuous function
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B
g is a bounded function
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C
g is bounded on [1,]
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D
g has a minimum value on[I,]
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Solution

## The correct option is B g is bounded on [1,∞]The graph for g(x) is shown in the figure. The value of g(0) is 0.The function g(x) is continuous everywhere except at g(x)=0.The function g(x) is unbounded because it assumes values in the interval (−∞,∞). For a function to be bounded, its values must always lie in a finite interval for all x.The function g(x) is bounded in the interval [1,∞) because it assumes values in a finite interval: (0,1] (limx→∞g(x)=0 and g(1)=1.   Suggest Corrections  0      Similar questions  Related Videos   Some Functions and Their Graphs
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