1.49. (!) Let f and g be functions from R to R. For the sum and product of f and g (see Definition 1.25), determine which statements below are true. If true, provide a proof; if false, provide a counterexample. a) If f and g are bounded, then f + g is bounded. b) If f and g are bounded, then fg is bounded. c) If f + g is bounded, then f and g are bounded. d) If fo

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1.49. (!) Let f and g be functions from R to R. For the sum and product of f
and g (see Definition 1.25), determine which statements below are true. If true,
provide a proof; if false, provide a counterexample.
a) If f and g are bounded, then f + g is bounded.
b) If f and g are bounded, then fg is bounded.
c) If f + g is bounded, then f and g are bounded.
d) If fg is bounded, then f and g are bounded.
e) If both f + g and fg are bounded, then f and g are bounded.
Y
Transcribed Image Text:1.49. (!) Let f and g be functions from R to R. For the sum and product of f and g (see Definition 1.25), determine which statements below are true. If true, provide a proof; if false, provide a counterexample. a) If f and g are bounded, then f + g is bounded. b) If f and g are bounded, then fg is bounded. c) If f + g is bounded, then f and g are bounded. d) If fg is bounded, then f and g are bounded. e) If both f + g and fg are bounded, then f and g are bounded. Y
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