If the function f ∶ R → R is given by f(x) = x² + 3x + 1 and g ∶ R → R is given by g(x) = 2x − 3,then find (i)fog and (ii)gof.
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Answer:
Step-by-step explanation:
f(x) = x² + 3x + 1
g(x) = 2x − 3
fog(x)
= f{g(x)}
= f(2x - 3)
= (2x - 3)² + 3(2x - 3) + 1
= 4x² - 12x + 9 + 6x - 9 + 1
= 4x² - 6x + 1
gof(x)
= g{f(x)}
= g(x² + 3x + 1)
= 2(x² + 3x + 1) - 3
= 2x² + 6x + 2 - 3
= 2x² + 6x - 1
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