Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = Four divided by x squared. + 9
1 answer:
• Interpretation I: Find f and g, so that 4 (f o g)(x) = ————— x² + 9 Well, there is more than one possibility. 4 For instance, It can be: f(x) = —— and g(x) = x² + 9 , x and then you have (f o g)(x) = f[ g(x) ] 4 (f o g)(x) = ———— g(x) 4 (f o g)(x) = ————— ✔ x² + 9 4 Another possibility for that composition: f(x) = ————— and g(x) = x² , x + 9 and for those, you get (f o g)(x) = f[ g(x) ] 4 (f o g)(x) = ——————— [ g(x) ]² + 9 4 (f o g)(x) = ————— ✔ x² + 9 As you can see above, there are many ways to find f and g, so the composition of those is (f o g)(x) = 4/(x² + 9) . —————• Interpretation II: Find f and g, so that 4 (f o g)(x) = —— + 9 x² 4 It can be: f(x) = x + 9 and g(x) = —— x² and then you have (f o g)(x) = f[ g(x) ] (f o g)(x) = g(x) + 9 4 (f o g)(x) = —— + 9 x² 2 or it could be also: f(x) = x² + 9 and g(x) = —— x and you have again (f o g)(x) = f[ g(x) ] (f o g)(x) = [ g(x) ]² + 9 (f o g)(x) = [ 2/x ]² + 9 (f o g)(x) = (2²/x²) + 9 4 (f o g)(x) = —— + 9 ✔ x² As you can see above, there are many ways to find f and g, so the composition of those is (f o g)(x) = (4/x²) + 9 . I hope this helps. =) Tags: <em>composite functions rational quadratic linear function algebra</em>
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