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Nested Functions

CONCEPTS

Tips

• When functions are nested, start inside and work outwards


Nested Function Notations

• f (g (x) [standard notation]

• (f ∘ g)(x) = f (g (x))

• (f * g)(x) = (fg)(x) = f(x) * g(x)


Inverse of a Function

• To solve for f⁻¹ (x), replace y with x & x with y

PRACTICE PROBLEMS

Question 1 What is f(g(x)) if g(x) = x - 3 & f(x) = x² + x?


-- Answer -- x² - 5x + 6

(x - 3)² + (x - 3) = x² - 5x + 6

ACT PRACTICE PROBLEMS

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