Question

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

(0, –2) (1, –1) (2, 0) (3, 3)

Answer 1

`\text{(3,3) is point of intersection of  } f^(-1)(x)=f(x)`

Explanation:

If f(x) and it's inverse function
`f^(-1)(x)` plot on same coordinate plane.

Both graph intersect at line y=x because y=x is line of symmetry of inverse function.

Intersection of
`f^(-1)(x)` and f(x) would be x and y coordinate same.

Therefore,
`f^(-1)(x)=f(x)=x`

We are given four options. Let we check each one.

Option 1: (0,-2)

x=0 and y=-2 , 0≠-2

This is false.

Option 2: (1,-1)

x=1 and y=-1 , 1≠-1

This is false.

Option 3: (2,0)

x=2 and y=0 , 2≠0

This is false.

Option 4: (3,3)

x=3 and y=3 , 3=3

This is true.

Thus, (3,3) is point of intersection of
`f^(-1)(x)=f(x)`