ich statement/s is always true for any real number t? f f(x) and h(x) are continuous at x = t, then is continuous at x = t. h(x) f f(x) + h(x) is continuous at x = t and f(x) = 0, then h(x) is continuous at x = a. f f(x) + h(x) is differentiable at x = t, then f(x) and g(x) are both differentiable at x = t. and b and c b and c a, b, and c only b

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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Which statement/s is always true for any real number t?
a. If f(x) and h(x) are continuous at x = t, then is continuous at x = t.
h(x)
b. If f(x) + h(x) is continuous at x = t and f(x) = 0, then h(x) is continuous at x = a.
c. If f(x) + h(x) is differentiable at x = t, then f(x) and g(x) are both differentiable at x = t.
I. a and b
II. a and c
III. b and c
IV. a, b, and c
V. only b
Transcribed Image Text:Which statement/s is always true for any real number t? a. If f(x) and h(x) are continuous at x = t, then is continuous at x = t. h(x) b. If f(x) + h(x) is continuous at x = t and f(x) = 0, then h(x) is continuous at x = a. c. If f(x) + h(x) is differentiable at x = t, then f(x) and g(x) are both differentiable at x = t. I. a and b II. a and c III. b and c IV. a, b, and c V. only b
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