1.2 Compute the composite functions f ºg and gºf if: (a) f(x) = 2x + 5, g(x) = x2 – 4 (b) f(x) = x2 +3, g(x) = 2x – 1
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Step-by-step explanation:
(a) f(x) = 2x + 5, g(x) = x2 – 4
f ºg=f(g(x))=f(x^2-4)=2(x^2-4)+5=2x^2-8+5=2x^2-3
gºf=g(f(x)) =g(2x + 5) =(2x + 5)^2 – 4=4x^2+40x+25-4
=4x^2+40x+ 21
(b) f(x) = x^2 +3, g(x) = 2x – 1
f ºg=f(g(x)) =f(2x – 1)
=(2x – 1) ^2+3=4x^2-4x+1+3=4x^2-4x+4
gºf=g(f(x) =g(x^2 +3)= 2(x^2 +3)-1= 2x^2 +6-1=2x^2 + 5
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