Question

The graph of f(x) is shown below. On a coordinate plane, a straight line has a negative slope and goes through (0, 6) and (3, 0). If f(x) and its inverse function, f Superscript negative 1 Baseline (x), are both plotted on the same coordinate plane, where is their point of intersection? (0,6) (1,4) (2,2) (3,0)

Answer 1

Answer:

The intersection point is (2,2)

Step-by-step explanation:

First let's find the equation of f(x), using the linear model:

$f(x) = ax + b$

Using the point (0, 6), we have:

$6 = a*0 + b\\b = 6$

Using the point (3, 0), we have:

$0 = a*3 + 6\\3a = -6\\a = -2$

So we have that $f(x) = -2x + 6$

To find f'(x) (the inverse of f(x)), we can substitute f(x) by x and x by f'(x) in the equation of f(x) and then isolate f'(x):

$x = -2f'(x) + 6\\2f'(x) = -x + 6\\f'(x) = -x/2 + 3$

Now, to find the intersection point, we need to calculate f(x) = f'(x):

$-2x + 6 = -x/2 + 3\\3x/2 = 3\\3x = 6\\x = 2$

And the y-value is:

$y = -2x + 6 = -2*2 + 6 = 2$

So the point is (2,2)