Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

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Domain: 1) f(0) = 8 2) f(3) = 3) g(-2) = -2 4) g(2) = 0 5) f(g(0)) = f(2) =0 6) f(g(-2)) = f(-2) =undefined 7) f(g(2)) = f(0) =8 8) f(g(-1)) = f(1) =3.

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Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x 2 + 2

Algebra II 6.4: Use Inverse Functions HW: p.442 (4-10 even, 16, 18, 22, 26)

Inverse Relations An inverse relation interchanges the input and output values (the x and y) of the original relation. An inverse relation interchanges the input and output values (the x and y) of the original relation. This means the domain and range This means the domain and range also change, since the domain is your also change, since the domain is your input and the range is your output. input and the range is your output.

Find the inverse of the relation. y = 3x – 5 y = 3x – 5 y = 5x + ½ y = 5x + ½

Find the inverse of the function. f(x) = x 3 – 2 f(x) = x 3 – 2 f(x)= f(x)=

Inverse Functions If both the relation and the inverse of the relation are functions, then they are called inverse functions. If both the relation and the inverse of the relation are functions, then they are called inverse functions.

Inverse functions Functions f and g are inverses of each other provided: Functions f and g are inverses of each other provided: f (g (x )) = x and g (f (x )) = x

Verify that f and g are inverse functions. f(x) = x + 4, g(x) = x – 4 f(x) = x + 4, g(x) = x – 4

Verify that f and g are inverse functions. f(x) =, g(x) = f(x) =, g(x) =

Sketch the graph of the inverse relation. Are these inverse functions?

Find the inverse of the function. f(x) = x 4 – 2 f(x) = x 4 – 2 f(x)= f(x)=