Can you guys please help with these questions I’m extremely stuck. It’s algebra 2 inverse functions.
1 answer:
9514 1404 393
Answer:
- The graph of a function and its inverse are reflections of each other in the line y=x
- For each ordered pair (x, y) in a function, the corresponding ordered pair in the inverse function is (y, x)
- see the attachment for the tables of values
Step-by-step explanation:
Consider the function and its inverse shown in the second attachment. The function is ...
f = {(a, 3), (b, 1), (c, 2)}
The inverse function is ...
f^-1 = {(3, a), (1, b), (2, c)}
You will notice that the "x" and "y" of each pair are swapped between the function and its inverse. <em>That is the point of an inverse function</em>. It gives you the input that caused the function to create the output. For example, the pair (3, a) in the above inverse function tells you that the output 3 was the result of an input of 'a' to the original function.
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On a graph, the swapping of input and output is essentially equivalent to relabeling the axes. If we keep the same x- and y-axis labels, it is equivalent to reflecting the function graph across the line y=x. That reflection is represented by the transformation (x, y) ⇒ (y, x).
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The point of the exercise here is for you to identify some ordered pairs of one of the functions and realize that the inverse function reverses their order. You are to see that the graph of the function and its inverse are reflections of each other across the diagonal line y=x.
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<u>Given</u>:
The given function is
We need to determine the value of the discriminant f and also to determine the distinct real number zeros of f.
<u>Discriminant</u>:
The discriminant can be determined using the formula,
Now, we shall determine the discriminant of the function
Substituting the values in the formula, we have;
Thus, the value of the discriminant of f is -92.
<u>Distinct roots:</u>
The distinct zeros of the function f can be determined by
(1) If , then the function has 2 real roots.
(2) If , then the function has 2 real roots ( or one repeated root).
(3) If , then the function has 2 imaginary roots (or no real roots).
Since, the discriminant is , then the function has no real roots or 2 imaginary roots.
Thus, the function has 2 imaginary roots.
Answer:
radical 232
Step-by-step explanation:
14^2+6^2=x^2
196+36= 232
radical 232
