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qwerty159
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Homework Statement
a) Determine the points where the function f (x) = (x + 3) / (x^2 − 3x − 10) is discontinuous. Then define a new function g that is a a continuous extension of f .
b) Determine what value of the constant k makes the Piecewise function
{ (x − k)/ (k^2 + 1) , x < 0
f (x) = { x^2 + k , x ≥ 0
continuous on lR. Justify your answer.
c) True or False: if f and g are both continuous at 0, then f ◦ g is also continuous at 0. Justify your answer by proving it (if true) or giving a counterexample (if false).
Homework Equations
The Attempt at a Solution
a) it is discontinuous at 5 and -2.Factored the denominator.
b) lim x-> 0- = k
& lim x-> 0+ = k
c) lim x-> 0 f(x) = f(0) & lim x-> 0 g(x) = g(0) so, f ◦ g is lim x-> 0 f(g(x)) = 0. It is continuous.
I hope I get a reply..No one is helping on other sites either. Thanks.
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