Let f(x) = (x-3)2-9, defined for all real x in the closed interval [3, 6]. ...

 

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Let f(x) = (x-3)2-9, defined for all real x in the closed interval [3, 6]. • Explain how the graph of the function f can be obtained from that of the standard parabola y = x². Sketch the graph of the function f and determine its range. • Explain why we know by inspection of its graph that the function f has an inverse function and obtain a formula for the inverse function f-¹(x). . What are the domain and range of f-1? Explain. Sketch the function f and its inverse on the same graph. Does the function g(x) = -f(x) have an inverse function? Explain. If so, find a formula for the inverse function g-¹(x) and sketch its graph. Let f(x) = (x-3)2-9, defined for all real x in the closed interval [3, 6]. • Explain how the graph of the function f can be obtained from that of the standard parabola y = x². Sketch the graph of the function f and determine its range. • Explain why we know by inspection of its graph that the function f has an inverse function and obtain a formula for the inverse function f-¹(x). . What are the domain and range of f-1? Explain. Sketch the function f and its inverse on the same graph. Does the function g(x) = -f(x) have an inverse function? Explain. If so, find a formula for the inverse function g-¹(x) and sketch its graph.