Question

Let y(x) = ax^{2} + bx + c. The function y(x) is not invertible, however, like the function f(x) = x^{2} we can make some restrictions on its domain to make it invertible. Hint: Think of the example (x^{2}) 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 lim
_{x→3}x^{2}−3x+1 = 1 using the definition of limit, that is, using ε and δ.

Step 1

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Step 2

a) First draw the graph for the given function as shown in below figure.

Step 3

From the above graph, *x* can have 2 value for each value of *y*.

So, horizontal test failed and the function is not invertible.

Make the function invertible with the help of restricting the domai...

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