Decide if the following claims are true or false, providing either a proof or counterex- ample...

 

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Decide if the following claims are true or false, providing either a proof or counterex- ample to justify each conclusion. Assume throughout that h is defined and continuous on all of R. (a) If h(x) 3 for all x > 0, then h(0) 3. Solution: Your solution goes here. (b) If h(y) = 0 for all y Q, then h(x) = 0 for all x R. Solution: Your solution goes here. (c) If there is some x0 = R such that h(x0) < 0, then there exist uncountably many points x where h(x) <0. Decide if the following claims are true or false, providing either a proof or counterex- ample to justify each conclusion. Assume throughout that h is defined and continuous on all of R. (a) If h(x) 3 for all x > 0, then h(0) 3. Solution: Your solution goes here. (b) If h(y) = 0 for all y Q, then h(x) = 0 for all x R. Solution: Your solution goes here. (c) If there is some x0 = R such that h(x0) < 0, then there exist uncountably many points x where h(x) <0.