Solve this: 5. On the interval I = [- 2, 2], the function 

f ( x ) = x + 1 e - 1 x + 1 x , X 0                                 0                                         x = 0                                        

a)is continuous for all  x I - 0
b)assumes all intermediate values from  f - 2   t o   f 2
 c) has a maximum value equal to 3/ e. 
all the above 


Dear Student,
Please find below the solution to the asked query:

fx=x+1e-1x+1xx00x=0x+1e-1x+1x=x+1e-1x+1xx>0x+1e--1x+1xx<0=x+1e-2xx>0x+1e0x<0=x+1e-2xx>0x+1x<0Nowlimx0- fx=limx0- x+1=0+1=1Also f0=0 GivenAs limx0- fxf0Hence function is discontiuous at x=0Otherwise both x+1 and e-1x+1x will be continuous as x=0 is the only doubtful point for e-1x+1x , hence their product x+1e-1x+1xwill be continuous.Hence optiona is correct.

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