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sonya
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if ur given a function f(x) and ur asked to find f^-1(y)...r u supposed 2 solve ur original eqn for y and then take the inverse of that? or isn't that just the same thing neways?...
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Originally posted by HallsofIvy
Since x= 3y- 4, 3y= x+ 4 and y= f-1(x)= (x+4)/3.
A function in mathematics is a rule or relationship that assigns one input value to one output value. It is used to describe the relationship between two or more quantities and to model real-world situations.
The domain of a function is the set of all possible input values for which the function is defined. It can be determined by looking at the restrictions on the input values in the function's equation or graph. The range of a function is the set of all possible output values for the corresponding input values. It can be determined by looking at the vertical values on the function's graph or by solving for the output values in the function's equation.
A linear function is a function where the output varies directly with the input. In other words, the output changes by a constant rate for every unit change in the input. A nonlinear function, on the other hand, does not follow this pattern and the output changes at a varying rate for different input values.
To graph a function, you first need to determine the domain and range of the function. Then, choose a few input values and use the function to calculate the corresponding output values. Plot these points on a coordinate plane and connect them with a smooth curve. Additionally, you can use transformations, such as shifting, stretching, or reflecting the graph to better understand the behavior of the function.
A function and its inverse function are two functions that "undo" each other. In other words, if the input of one function is the output of the other, and vice versa, then they are inverse functions. The inverse function can be obtained by switching the input and output variables in the original function's equation. The domain and range of the inverse function are also switched from the original function.