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Answer:
- Domain & Range (also of inverse function): all real numbers except 0.5. The graph of the inverse is the same graph.
- Domain & Range (also of inverse function): all real numbers. The graph of the inverse is y = 1/2x -2.5, a line from (-5, -5) through (5, 0).
Step-by-step explanation:
1. The inverse function is a reflection of the function across the line y=x. Since the function is already symmetric about that line, the inverse function is the same as the function.
The domain is the horizontal extent of the graph. The function is defined everywhere except at x=0.5, so that value is excluded from the domain. Since the function is its own inverse, that value is also excluded from the range.
Domain and Range (of the function and its inverse): all real numbers except 0.5
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2. The domain and range of any linear function is all real numbers. The inverse function of a linear function is also a linear function.
Domain and range (of the function and its inverse): all real numbers.
The inverse function is the reflection of the line across the line y=x. That is, its graph will go through (-5, -5) and (5, 0). The corresponding equation is ...
y = 1/2x -2.5
This graphs as a line from the lower left corner to the middle of the right side of the graph shown. In the attachment, the inverse function is the blue line.
