Find fog and g • f, where f and g are functions defined from R to R f(x) = x2+2x+1 g(x) = 6x+4
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Given that,f(x) = x2 + 3x + 1,g(x) = 2x - 3
(i) fog = f(g(x))
= f(2x-3)
= (2x-3)2 + 3(2x-3)+1
= 4x2 - 12x + 9 + 6x - 9 + 1
= 4x2 - 6x + 1
(ii) gof = g(f(x)
= g(x2+3x+1)
= 2(x2+3x+1)-3
= 2x2 + 6x - 1
(iii) fof = f(f(x))
= f(x2 + 3x + 1)
= (x2 + 3x + 1)2 + 3(x2 + 3x + 1) + 1
= x4 + 9x2 + 1 + 6x2 + 6x + 2x2 + 3x2 + 9x + 3 + 1
= x4 + 6x3 + 14x2 + 15x + 5
(iv) gog = g(g(x))
= g(2x-3)
= 2(2x-3)-3
= 4x - 6 - 3
= 4x - 9
Step-by-step explanation:
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