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AP Calculus AB

AP Calculus AB. Day 6 Section 5.3. Inverse Functions. If f ( g (x)) = x and g ( f (x)) = x then f (x) and g (x) are inverses. Domain of f (x) = Range of f -1 (x) Range of f (x) = Domain of f -1 (x) Inverses are symmetric about y = x.

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AP Calculus AB

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  1. AP Calculus AB Day 6 Section 5.3 Perkins

  2. Inverse Functions • If f(g(x)) = x and g(f(x)) = x then f(x) and g(x) are inverses. • Domain of f(x) = Range of f -1(x) Range of f(x) = Domain of f -1(x) • Inverses are symmetric about y = x. • A function can only have an inverse if it is 1-to-1. 2 ways to check 1-to-1: a. horizontal line test b. is it always inc or dec? Note: if a function isn’t 1-to-1 we can change its domain to make it 1-to-1.

  3. You could… Graph each and show symmetry about y = x. Show that both f(g(x)) = x and g(f(x)) = x. Find the inverse of one of the functions and compare. To find an inverse: Swap x & y. Solve for y. Domain of f -1(x) = Range of f(x). 1. Show that these functions are inverses: These functions are inverses.

  4. Can these functions have inverses? This function can’t have an inverse. This derivative is always positive, so y is always increasing. This derivative changes signs, so y increases and decreases. This function can have an inverse. This function can’t have an inverse. …unless we limit its domain to all positives or all negatives.

  5. 5. Find the inverse of This function isn’t 1-to-1. Limit its domain.

  6. AP Calculus AB Day 6 Section 5.3 Perkins

  7. Inverse Functions • If f(g(x)) = x and g(f(x)) = x then f(x) and g(x) are inverses. • Domain of f(x) = Range of f -1(x) Range of f(x) = Domain of f -1(x) • Inverses are symmetric about y = x. • A function can only have an inverse if it is 1-to-1. 2 ways to check 1-to-1: a. b.

  8. 1. Show that these functions are inverses:

  9. Can these functions have inverses?

  10. 5. Find the inverse of

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