Question

Which statement correctly identifies a point on the graph of f¹(x)?O The point (4,-7) is on the graph of f(x), so the point (7,-4) will be on the graph of f¹(x).The point (-2, 15) is on the graph of f(x), so the point (2, -15) will be on the graph of f¹(x).The point (-4, 19) is on the graph of f(x), so the point (-4, -19) will be on the graph of f¹(x).The point (10, -14) is on the graph of f(x), so the point (-14, 10) will be on the graph of f¹(x).

Answer 1

The correct statement that identifies a point on the graph of f¹(x) is: C. The point (-4, 19) is on the graph of f(x), so the point (-4, -19) will be on the graph of f¹(x).'

What is the point ?

A point on the graph of f(x) is mentioned in the statement: (-4, 19). The graph of f(x) has the point (-4, 19), indicating that y = 19 is the result of entering x = -4 into the function f(x).

The next part of the statement refers to the inverse function f(x) and states that the point (-4, -19) will be on the graph of f¹(x). We must change the original point's x and y coordinates (-4, 19) in order to find the inverse function. Hence, (19, -4) becomes (-4, 19).

As a result, the point (19, -4) is located on the f¹(x) graph, indicating that y = -4 is the result of entering x = 19 into the inverse function f¹(x).

Therefore the correct option is C.

Answer 2

Fom the table given in the question, we are asked to determine the statement that correcty identifies a point of the graph of f^-1 (x)

One thing we must first note about a function is that, for an inverse function, x and y switches values.

That is, for every (x, y) of f(x) the inverse function will have (y, x) of f^-1 (x)

So, the statement from the option that correctly identifies a point on the graph of f^-1(x) is:

The point (4, -7) is on the graph of f(x), so the point (7, -4) will be on the graph of f^-1(x).

Therefore, the correct option is the first option.