1 2 Please helpSolutiona Let us divide the plot of g into th

Please help

a) Let us divide the plot of g into three segments:

A: 0 < x < 1

B: 1 < x < 4

and C: 4 < x < 6

For region A, the slope is m = (2-1)/(1-0) = 1

So, the equation of the line will be: g(x) - 1 = 1(x - 0)

therefore g(x) = x + 1 [for region A].

=> g(3x) = 3[x + 1] = 3x + 3

=> for A, y = 2(3x + 3) = 6x + 6

Hence y will be a straight line from x = 0 to x = 1 with y values ranging from 6 < y < 12.

for region B:

m = -1

therefore g(x) - (-1) = -1[x - 4]

=> g(x) = - x + 3

so g(3x) = -3x + 9

=> y = 2(-3x + 9) = -6x + 18

hence y is a straight line with values, 12 < y < - 6

for region C:

m = 1/2

therefore , g(x) - 0 = 1/2[x - 6]

g(x) = 0.5x - 3

g(3x) = 1.5x - 9

=> y = 2[1.5x - 9] = 3x - 18

therefore y is a straight line with values from - 6 < y < 0

b) Regions are same.

So, for Region A:

g(x) = x + 1

therefore y = g(x + 2) = (x + 2) + 1 = x + 3

hence 3 < y < 4

for Region B:

g(x) = - x + 3

y = g(x + 2) = - [x + 2] + 3 = - x + 5

hence 4 < y < 1

for Region C:

g(x) = 0.5x - 3

y = g(x + 2) = 0.5[x + 2] - 3 = 0.5x - 2

hence 0 < y < 1