I posted both the questions and solutions to problems a and b. I only need those

Question

I posted both the questions and solutions to problems a and b. I only need those two problems explained. The solutions are in the screenshot, but I don't know how to find them. If you could show the reasoning behind these answers, that would be great! Picture posted below.

If f 3,-5), 2, -4), (0, -5), (1,3), (2, 0), (4, 7) and g f( 4, 8), (-3,-8), (-2, -3), (0, l), (,4)), find (a) fog and (b) g of and, if possible, evaluate (c) (fog)(1), (d) (g of)(-3), (e) (fog)(-4), and (f (g of)(2). (a) fog Ho 2,- 5), (0, 3), 7)

Explanation / Answer

Domain of f = {-3,-2,0,1,2,4}

range of f = {-5,-4,3,0,7}

Domain of g = {-4,-3,-2,0,1}

range of g = {-8,8,-3,1,4}

for [fog = f(g(x))]

range of g = domain of f

possible set = {-3, 1, 4}

So domain of f = {-2, 0, 1}

and their range will be = {-5,3,7}

So, fog = [(-2, -5), (0,3),(1,7)}

Similarly

gof = g(f(x))

domain of g = range of f

possible set = {-4, 0}

domain of gof = {-2, 2}

and their range will be = {8, 1}

Let me know if you have any doubt.

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