If f(x) = (1  x)² and g(x) = 3  x, find f(g(x)) and g(f(x)).
To find f(g(x)), substitute what g(x) is.....(3  x), in for x, into f(x).
f(g(x)) = [1  (3  x)]² {substituted (3  x), in for x, into f(x)} = (1  3 + x)² {distributed negative sign through parentheses} = (2 + x)² {combined 1 and 3} = (2 + x)(2 + x) {squared the binomial} = 4  2x  2x + x² {used FOIL method / distributive property} = x²  4x + 4 {combined like terms and wrote in standard form} To find g(f(x)), substituted what f(x) is .....(1  x)², in for x, into g(x). g(f(x)) = 3  (1  x)² {substituted (1  x), in for x, into g(x)} = 3  (1  x)(1  x) {squared the binomial} = 3  (1  x  x + x²) {used FOIL method / distributive property} = 3  (1  2x + x²) {combined like terms} = 3  1 + 2x  x² {distributed negative sign through parentheses} = x² + 2x + 2 {combined like terms and wrote in standard form} Ask Algebra House
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