SOLUTION: Find two functions, f(x) and g(x) such that (fog)(x)=h(x) or (gof)(x)=h(x) where h(x)= sq. rt. of x squared minus 2 over x squared plus 3, and verify.

Question 443313: Find two functions, f(x) and g(x) such that (fog)(x)=h(x) or (gof)(x)=h(x) where h(x)= sq. rt. of x squared minus 2 over x squared plus 3, and verify.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find two functions, f(x) and g(x) such that (fog)(x)=h(x) or (gof)(x)=h(x) where h(x)= sq. rt. of x squared minus 2 over x squared plus 3, and verify.
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fog(x) = sqrt[(x^2-2)/(x^2+3)]
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Let g(x) = (x^2-2)/(x^2+3)
Let f(x) = sqrt(x)
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Then fog(x) = f[g(x)] = f[(x^2-2)/(x^2+3)] = sqrt[(x^2-2)/(x^2+3)]
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Cheers,
Stan H.
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