function f(x)f(x)
A function f(x)f(x) includes the points (2, 3)(2, 3), (−5, 1)(−5, 1), and (10, −3)(10, −3) in its graph. Based on this, which of the following points must be included in the graph of f−1(x)f−1(x)?
Choose TWO correct answers.
A.(3, 4)(3, 4)
B.(−3, 10)(−3, 10)
C.(−1, 5)(−1, 5)
D.(−3, −2)(−3, −2)
E.(−5, 1)(−5, 1)
F.(3, 2)(3, 2)
Sample Solution
The graph of the inverse function is obtained by reflecting the graph of the original function over the line y = x. This means that the x-coordinate of each point on the original function becomes the y-coordinate on the inverse function, and vice versa.Full Answer Section
Therefore, the points that must be included in the graph of f−1(x)f−1(x) are:
- (3, 2) (from the point (2, 3))
- (1, −5) (from the point (−5, 1))
- (−3, 10) (from the point (10, −3))
So, the correct answers are F and B.