True or False?

Question

If the inverse function of f exists, and the graph of f has a y-intercept, the y-intercept of f is an x-intercept of f^-1

Answer 1

This exact question was answered yesterday.

Are you Sam too?

Try an example to see if this is true.

f(x) = 3x - 1
So, f(x) has y-intercept = -1

To find inverse of f(x),
y = 3x - 1
x = 1/3 y + 1/3
y = 1/3 x + 1/3
f^-1 = 1/3 x + 1/3

To find x-intercept,
y = 1/3 x + 1/3
0 = 1/3 x + 1/3
-1/3 = 1/3 x
x = -1

So, f^-1 has an x-intercept = -1.

So, True or False?

Answer 2

False? Because -1 doesn't equal 1/3? Still don't get it

Answer 3

Is it false because -1 isn't equal to 1/3

Answer 4

the y-intercept of f(x) is an x-intercept of f^-1

Look at the example I did for you.

What is the y-intercept of f(x)?

What is the x-intercept of f^-1?

Are they the same?

If yes, true.
If not, false.