Let y(x) = ax2 + bx + c. The function y(x) is not invertible, however, like the function f(x) = x2 we can make some restrictions on its domain to make it invertible. Hint: Think of the example (x2) given above. Find the largest possible domain where y(x) is invertible Find its inverse function using this domain Check that it is indeed the inverse function by verifying the identity y−1(y(x)) =y(y−1(x)) = x Show limx→3 x2 −3x+1 = 1 using the definition of limit, that is, using ε and δ.

Let y(x) = ax2 + bx + c. The function y(x) is not invertible, however, like the function f(x) = x2 we can make some restrictions on its domain to make it invertible. Hint: Think of the example (x2) given above. Find the largest possible domain where y(x) is invertible Find its inverse function using this domain Check that it is indeed the inverse function by verifying the identity y−1(y(x)) =y(y−1(x)) = x Show limx→3 x2 −3x+1 = 1 using the definition of limit, that is, using ε and δ.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 55E

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