How Do I Solve These Kind Of Questions: 1) F(x)=2x+3, G(x)=x^2-1, Find ...

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SOLUTION: How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3) 2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x) 3) f(x)= root x, g(x)=-x^2-2, find (fog)(x) 4) f(x)=x^ Algebra -> Functions -> SOLUTION: How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3) 2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x) 3) f(x)= root x, g(x)=-x^2-2, find (fog)(x) 4) f(x)=x^ Log On
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Question 787140: How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3) 2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x) 3) f(x)= root x, g(x)=-x^2-2, find (fog)(x) 4) f(x)=x^2-1, g(x)=x^2+1, find (fog)(x) - (gof)(x) Thank you. Answer by Edwin McCravy(19929) About Me (Show Source): You can put this solution on YOUR website! How do I solve these kind of questions: 1) f(x)=2x+3, g(x)=x-1, find (f∘g)(3) (f∘g)(3) = f(g(3)) Find g(3) by substituting x=3 in g(x) g(x)=x-1 g(3)=3-1 g(3)=9-1 g(3)=8 f∘g(3) = f(g(3)) = f(8) find f(8) by substituting x=8 in f(x): f(x)=2x+3 f(8)=2(8)+3 f(8)=16+3 f(8)=19 So f∘g(3) = 19 ------------------------- 2) f(x)=3x-2, g(x)=%28x%2B2%29%2F3, find (f∘g)(x) (f∘g)(x) = f(g(x)) = f%28%28x%2B2%29%2F3%29 Find f%28%28x%2B2%29%2F3%29 by replacing x by %28x%2B2%29%2F3 in f(x) f(x)=3x-2 f%28%28x%2B2%29%2F3%29=3%28%28x%2B2%29%2F3%29-2 f%28%28x%2B2%29%2F3%29=(x+2)-2 f%28%28x%2B2%29%2F3%29=x+2-2 f%28%28x%2B2%29%2F3%29=x So (f∘g)(x) = x --------------------------- 3) f(x) = √x, g(x)=-x-2, find (f∘g)(x) (f∘g)(x) = f(g(x)) = f(-x-1) Find f(-x-1) by replacing x by -x-1 in f(x) f(x) = √x f(-x-1) = √-x-1 So (f∘g)(x) = √-x-1 -------------------------- 4) f(x)=x-1, g(x)=x+1, find (f∘g)(x) - (g∘f)(x) (f∘g)(x) - (g∘f)(x) = f(g(x)) - g(f(x)) = f(x+1) - g(x-1) = [(x+1)-1] - [(x-1)+1] = [x+2x+1-1] - [x-2x+1+1] = [x+2x] - [x-2x+2] = x+2x-x+2x-2 = 4x-2 Edwin

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