Please help!! I cant find the last two

Question

For each pair of functions, find  and  . Determine the domain of  and the domain of . Show your work



4.  and 

5.  and 

Answer 1

f=5x+2, g=x^2+1

f(g(x)) = (fog)(x)= 5(x^2+1)+2 = 5x^2 +7

domain is all reals

g(f(x)) = (God)(x) = (a seemingly religious function?? OMG, accidentally hit d instead of f and the deity pops up out of nowhere)) = g(5x+2)= (5x+2)^2 +1 = 25x^2 +20x +5

domain is all reals

f=2x^2 -4x +21, g=x+3

f(g(x)) = 2(x+3)^2 -4(x+3) +21 = 2x^2+12x+18-4x-12+21= 2x^2+8x+27=(fog)(x) a foggy problem, but the fog lifts and you can drive safely again

g(f(x) = g(2x^2-4x+21) = 2x^2-4x +24 = (Gof)

Answer 2

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