SOLUTION: Prove that f(x)=√x+8, domain [-8,∞) and g(x)= x^2-8, domain [0,∞) are inverses of each other using algebraic methods
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Question 823127: Prove that f(x)=√x+8, domain [-8,∞) and g(x)= x^2-8, domain [0,∞) are inverses of each other using algebraic methods
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Prove that f(x)=√x+8, domain [-8,∞) and g(x)= x^2-8, domain [0,∞) are inverses of each other using algebraic methods.
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Note:: f and g are inverses if fog(x) = gof(x) = x
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fog(x) = f[g(x)] = f[x^2-8] = sqrt(x^2-8+8) = sqrt(x^2) = x
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gof(x) = g[f(x)] = g[sqrt(x+8)] = (sqrt(x+8))^2-8 = x+8-8 = x
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Cheers,
Stan H.
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