Question

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?

Answer 1

Answer:

(2,2)

Step-by-step explanation:

step 1

Find the equation of f(x)

is a line that passes through the points (0,6) and (3,0)

Find the slope

$m=(0-6)/(3-0)=-2$

The function f(x) in slope intercept form is equal to

$f(x)=-2x+6$

step 2

Find the inverse

Let y=f(x)

$y=-2x+6$

Exchange the variables x for y and y for x

$x=-2y+6$

Isolate the variable y

$2y=-x+6$

$y=-0.5x+3$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=-0.5x+3$

step 3

Solve the system of equations

$f(x)=-2x+6$

$f^{-1}(x)=-0.5x+3$

equate both functions

$-0.5x+3=-2x+6$

solve for x

$2x-0.5x=6-3$

$1.5x=3$

$x=2$

substitute the value of x in any of the functions

$f(x)=-2(2)+6=2$

The solution is the point (2,2)

therefore

Their point of intersection is (2,2)

Answer 2

Answer:

C. (2,2)

Step-by-step explanation: