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Math 1304 Calculus I

Math 1304 Calculus I. 1.6 Inverse Functions. 1.6 Inverse functions. Definition: A function f is said to be one-to-one if f(x) = f(y) implies x = y. It never takes on the same value twice

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Math 1304 Calculus I

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  1. Math 1304 Calculus I 1.6 Inverse Functions

  2. 1.6 Inverse functions • Definition: A function f is said to be one-to-one if f(x) = f(y) implies x = y. • It never takes on the same value twice • Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than once.

  3. Inverse Functions • Definition: Let f and g be functions. They are said to be inverse if y = f(x) ↔ g(y) = x • Theorem: If f is a one-to-one function then it has an unique inverse. • Notation: the inverse of f is denoted by f-1

  4. Rules for inverses • f-1(f(x)) = x, for all x in the domain of f • f(f-1 (x)) = x, for all x in the domain of f-1

  5. Finding an inverse • Write y = f(x) and solve for x in terms of y.

  6. Logarithms are inverse to exponentials • loga(y) = x iff y = ax

  7. Laws for logarithms • See page 64

  8. Natural Logarithms • Natural = base e • ln(x) = loge(x)

  9. The number e • e = 2.718281828… is a special number that is used as a base for exponential functions in calculus

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