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5.3 The Derivative of an Inverse Function. Remember…. If a function f has an inverse function f -1 , Then f ( a ) = b implies that f -1 ( b ) = a . x ’s and y ’s switch!.
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Remember… • If a function f has an inverse function f-1, Then f (a) = b implies that f-1(b) = a. • x’s and y’s switch!
The Derivative of f -1(x):So…The derivative of the inverse is the reciprocal of the derivative of the original
Ex 1) Given that y = f(x) = x3 + 2x – 3 is a one-to–one function, and thus has an inverse, find (f-1)'(0).
Ex 2) • Find , if: & .
Ex 3) Find y:
Ex 4) Find y:
Ex 5) Find y:
HW – 5.3 pg. 349# 71 – 75 odds, 95 5.6 pg. 378# 41 – 49 odds, 61 & 63
Ex 1) Let g be the function which converts from Fahrenheit to Celsius. Then g (F) = C = (5/9) (F – 32) Find g-1:
Ex 3) • Find , if: , , & .
