Question 1199936: Given f(x)= 2x^2-x-2 and g(x)=x+2, find f ° g and g ° f.
Answer by algebrahouse.com(1659)   (Show Source):
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f(x) = 2x² - x - 2
g(x) = x + 2
f(g(x))
= 2(x + 2)² - (x + 2) - 2 {substituted g(x), in for x, into f(x)}
= 2(x + 2)(x + 2) - (x + 2) - 2 {when you square a binomial, multiply it by itself}
= 2(x² + 4x + 4) - x - 2 - 2 {used distributive property to remove parentheses}
= 2x² + 8x + 8 - x - 4 {used distributive property and combined -2 and -2}
= 2x² + 7x + 4 {combined like terms}
g(f(x))
= (2x² - x - 2 )+ 2 {substituted f(x), in for x, into g(x)}
= 2x² - x - 2 + 2 {removed parentheses}
= 2x² - x {combined like terms}
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