below is the entire graph of function f. graph f⁻¹, the inverse of f.
below is the entire graph of function f. graph f⁻¹, the inverse of f.
Answer
Explanation:
Step1: Recall inverse - graph property
The graph of (y = f^{-1}(x)) is the reflection of the graph of (y = f(x)) about the line (y=x).
Step2: Identify key points on (f)
Let's assume some key - points on (y = f(x)). For example, if ((x_1,y_1)) is on (y = f(x)), then ((y_1,x_1)) is on (y = f^{-1}(x)). Suppose a point on (f) is ((- 3,0)), then a point on (f^{-1}) is ((0,-3)).
Step3: Reflect all points
Take all the points on the graph of (y = f(x)) and reflect them across the line (y = x). Connect the reflected points to form the graph of (y = f^{-1}(x)).
Answer:
To graph (f^{-1}), reflect the graph of (f) about the line (y = x) by swapping the (x) and (y) - coordinates of all points on the graph of (f) and then connecting the new points.