if the point a,b lies on the graph y=f of x, the graph of y= f inverse of x must contain what point....

Question

if the point a,b lies on the graph y=f of x, the graph of y= f inverse of x must  contain what point

Answer 1

Mark gave a good answer, that is the very definition of inverse functions.

To make this more visual, more intuitive, draw a graph of the identity function, y = x, which is just a straight line at an angle of 45 degrees, passing through the origin. The two graphs of f(x) and its inverse are reflections of each other across this line. Any point on one side of the line (say 4,7), when folded over the line, becomes (7,4). If you actually draw this sketch and fold the paper at the y = x line, this will burn the image into your mind and you will never forget!

These questions seem hard and mysterious, but they really make sense.  Good luck!

Answer 2

y = f(x)

 

y = x

 

y = b

x = a

 

Inverse means that you switch places with x and y.  Therefore, you have

 

x = y

 

Your point is (b,a).

Answer 3

If (a, b) lies on the graph of y = f(x), then f(a) = b. 

 

By definition the inverse of the function, f^-1(x), is such that f^-1(b) = a.

 

Therefore the point (b, a) must be on the graph of f^-1(x).