If f (x) =2x²+3 g(x)=5x_2,then find a》f°g b》g°f
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Answer :
a). (fog)(x) = 50x² - 40x + 11
b). (gof)(x) = 10x² + 13
Solution :
- Given : f(x) = 2x² + 3 , g(x) = 5x - 2
- To find : a). fog = ? , b). gof = ?
a). (fog)(x) = f(g(x))
=> (fog)(x) = f(5x - 2)
=> (fog)(x) = 2(5x - 2)² + 3
=> (fog)(x) = 2(25x² - 20x + 4) + 3
=> (fog)(x) = 50x² - 40x + 8 + 3
=> (fog)(x) = 50x² - 40x + 11
b). (gof)(x) = g(f(x))
=> (gof)(x) = g(2x² + 3)
=> (gof)(x) = 5(2x² + 3) - 2
=> (gof)(x) = 10x² + 15 - 2
=> (gof)(x) = 10x² + 13
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