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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