Only the problem that is underlined 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.
Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Only the problem that is underlined
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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images