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Math1011_Week02_15_16_21

# Math1011_Week02_15_16_21 - Math1011 Learning Strategies...

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Math1011 – Learning Strategies Center Section 1.6 9/9/2009 The graph shows the graph of a function y = f(x). Draw in the line y = x and use symmetry with respect to the line y = x to add the graph of f -1 (x) to your sketch. Identify the domain and range of f -1 (x). -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 x = - π /2 x = π /2 Domain of f(x) Range of f(x) Domain of f -1 (x) Range of f -1 (x) Any guess as to what common function f(x) is?

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Math1011 – Learning Strategies Center Section 1.6 1 The graph shows the graph of a function y = f(x). Draw in the line y = x and use symmetry with respect to the line y = x to add the graph of f -1 (x) to your sketch. Identify the domain and range of f -1 (x). -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 x = - π /2 x = π /2 y = π /2 y = - π /2 Domain of f(x) (- π /2, π /2) Range of f(x) (- , ) Domain of f -1 (x) (- , ) Range of f -1 (x) (- π /2, π /2) Any guess as to what common function f(x) is? f(x) = tan(x) restricted domain of - π /2 < x < π /2 (Doc #011w.16.01t)
Math1011 Section 1.6 2 Find the domain, range, and inverse function for: ( ) 4 x f x e =

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Math1011 Section 1.6 2 Find the domain, range, and inverse function for: ( ) 4 x f x e = x Domain: 4e is valid for all x Domain: (- , ) or we can write - x ∞ ∞ ∞ < < ∞ : 4 is always positive : (0, ) or we can write 0 x Range e Range y < < ∞ 1 4 1 4 1 4 1 4 1 4 1 4 Inverse Function: solve for x in terms of y 4 ln ln ln ln ln ln switch x and y ln Note: domain (0, ) range (- , ) Range of inverse function is domain of original functi x x x y e y e y e y x e y x x y y x = = = = = = =
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Math1011_Week02_15_16_21 - Math1011 Learning Strategies...

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