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Inverse Relations Remember, a relation is a mapping of input values to output values. An inverse relation maps the outputs back onto the inputs. (The domain and range switch.) Its graph is a reflection of the original relation over the line y = x.
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Finding an Inverse Relation1. Switch x and y.2. Solve for y.Example: Find the inverse of y = 2x - 4
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Inverse Functions If both the original relation and its inverse are functions, they are inverse functions. Functions f and g are inverses if: f(g(x)) = x and g(f(x)) = x Function g is then called f-1 (read “f inverse”)
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Verifying Inverse Functions Show that Example:Verify thatare inverses.
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Inverses of Nonlinear Functions f(x) = x2 g(x) = x3 + 2 x = y2The inverse of f(x) = x2 is not a function.If we restrict the domain of f(x) to one side, (say x 0 or x 0 ) then it is.
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Finding an Inverse Power Function We still switch x and y, then solve for y. Example: Find the inverse of f(x) = x2, x 0
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Horizontal Line Test Used to determine if the inverse of f is a function. If a horizontal line crosses f more than once, then f inverse is not a function.
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Finding an Inverse Function Example: For the function determine if the inverse is a function, then find the inverse.
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Your Turn! For the function determine whether the inverse is a function and find the inverse.
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