  Problem 3 - Let g(x) and h(x) be the following piece-wise defined functionsx1, if x

Question help_outlineImage TranscriptioncloseProblem 3 - Let g(x) and h(x) be the following piece-wise defined functions x1, if x<0 if 0 1 g(ax) IC 2 , if 1
Step 1

Left hand limit of x=0 is=0+1=1

Right hand limit of x=0 is= -infinity

So, at x=0 it is discontinuous help_outlineImage Transcriptioncloselimh(x) x-0 = lim (x+1) X0 -0+1 lim h(x) x-0 lim In x x0 =-oo fullscreen
Step 2

Left hand limit of x=1 is =0

Right hand limit of x=1 is = 1

So h(x) is discontinuous at x=1

Answer(a): h(x) is discontinuous at x=0 and x=1 help_outlineImage Transcriptioncloselimh(x) x1 limln(x) x-1 =In(1) =0 lim h(x) x1 =lm (2-x) x1 -2-1 =1 fullscreen
Step 3

Both at x=0 and x=1 it is left continuous , because equality holds at left...

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Continuity 