we have a function

f(x) = x^2 - 3 for x<2, 6/x for x>=2 (x greater or equal to 2)

i've shown that the limits of this function from the left and right of 2 respectively are 1 and 3. (given in qn)

also shown that*if any function is continuous on [a,b] then it is bounded on [a,b]*

now i need to find out whether i can

1) use the above theorem (in bold) to the function f(x) on the interval [0,5]

2) determine whether f(x) is bounded on [0,5]

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my thoughts - clearly the function isn't continuous at 2, but it is piecewise continuous on the interval, so.... it's okay to use the theorem? or does it have to be continuous everywhere?

apologies for the lack of latex

thank youuu