Function Inverses (4.3) An inverse relation interchanges the input ...

Function Inverses (4.3)
An inverse relation interchanges the input and output values
of the original relation.
Functions f and g are inverse functions of each other
provided f(g(x)) = x and g(f(x)) = x. The function g is denoted
f ­1 , read as "f inverse."
An inverse of a function f is also a function if and only if no
horizontal line intersects the graph of f more than once.
Mar 4­9:13 AM
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Verifying Inverse Functions
To verify that two functions are inverses of each other, show
that f(g(x)) = x AND g(f(x)) = x.
Verify that the two functions are inverses of each other.
1) f(x) = x ­ 3 and g(x) = x + 3
2) f(x) = 1 / 2 x + 3 and g(x) = 2x ­ 6
Mar 4­9:16 AM
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Finding the Inverse of a Function
1) Rewrite "f(x) = " as" y = "
2) Switch x and y
3) Solve for y
4) Rewrite as f ­1 (x) =
Find the inverse of each function.
1) f(x) = 3x ­ 1 2) f(x) = 2 / 3 x ­ 4
Mar 4­9:21 AM
3

Find the inverse of each function.
3) f(x) = 3x 2 ­ 8 4) f(x) = x 5
5) f(x) = 2x 3 + 7 6) f(x) = 3 / x
Mar 4­9:38 AM
4

Find the inverse of the function.
1) f(x) = ­5x + 2 2) f(x) = 2x 4 ­ 3
3) f(x) = 4 / x 4) f(x) = (x + 1) 2
5) Verify the two functions are inverses:
f(x) = 4x + 3 and g(x) = 1 / 4 x ­ 3 / 4
Mar 4­9:43 AM
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HOMEWORK
Page 118 #1­14
Mar 4­9:47 AM
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