Given f (x) = 2x + 3 and g(x) = x2 – 5x + 6, compute (fog)(x) =

(fog)(x) = 2x² - 10x + 15

Step-by-step explanation:

Let us solve our question

∵ f(x) = 2x + 3

∵ g(x) = x² - 5x + 6

→ We need to compute (fog)(x)

∴ Substitute x in f(x) by g(x)

∵ (fog)(x) = 2(x² - 5x + 6) + 3

→ Multiply the bracket by 2

∵ 2(x² - 5x + 6) = 2(x²) - 2(5x) + 2(6)

∴ 2(x² - 5x + 6) = 2x² - 10x + 12

→ Substitute it in the composite function above

∴ (fog)(x) = 2x² - 10x + 12 + 3

→ Add the like terms 12 and 3

∴  (fog)(x) = 2x² - 10x + 15

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so

step-by-step explanation:

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a reflection across the x axis and a 90 degree rotation left and right.