Problem 5 (3 points each) Let and g be bounded functions on [a, b]. (a) Prove...

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Problem 5 (3 points each) Let and g be bounded functions on [a, b]. (a) Prove the triangle inequality for the uniform norm, || + 9||u ||f||u+9u (b) Using your result in (a), prove the reverse triangle inequality for the uniform norm, ||fu-9u|| 9||u (Hint: Your proof will look very similar to the proof of the reverse triangle inequality for the absolute value) Problem 5 (3 points each) Let and g be bounded functions on [a, b]. (a) Prove the triangle inequality for the uniform norm, || + 9||u ||f||u+9u (b) Using your result in (a), prove the reverse triangle inequality for the uniform norm, ||fu-9u|| 9||u (Hint: Your proof will look very similar to the proof of the reverse triangle inequality for the absolute value)