Graph both functions separately, preferably using different colors for each graph. Then, using a third color, or a marker pen, go over the parts of the two graphs for which x ≥ 0 and x ≠ 1. From that graph it should be evident what the range of the sum function is.Coco12 said:
The graph of the product function is a parabola that opens downward. You should already have a technique for finding the vertex of a parabola. Let's say that the vertex is at (a, b). Then the range will be {y| -∞ < y ≤ b}.Coco12 said:
Mark44 said:
The graphs don't show the sum or difference of the two functions. Those (sum or difference) are the graphs of interest here.Coco12 said:
Mark44 said:
A composition function is a mathematical operation that combines two functions to create a new function. It is denoted by (f ∘ g)(x) and is read as "f of g of x." It means that the output of the inner function, g(x), becomes the input for the outer function, f(x).
To find the domain of a composition function, you must first find the domain of the inner function, g(x). Then, you must determine which values of x from g(x)'s domain will result in a real output for the outer function, f(x). The resulting values will be the domain of the composition function.
The range of a composition function is the set of all possible output values from the function. To find the range, you must evaluate the composite function for different input values and determine the resulting output values.
A composition function is one-to-one if every input value has a unique output value. To determine this, you can graph the function and use the horizontal line test. If any horizontal line intersects the graph at more than one point, the function is not one-to-one.
No, a composition function cannot have an empty domain or range. Since the output of the inner function becomes the input for the outer function, there must be at least one value in the domain of the inner function that will result in a real output for the outer function.