Question

The graph of f(x) is shown below.

if f(x) and it's inverse function, f-1(x), are both plotted on the same coordinate plane, where is their point of intersection?

a. (0, 6)
b. (1, 4)
c. (2, 2)
d. (3, 0)​

Answer 1

Answer:

(1,4)

Step-by-step explanation:

Answer 2

If f(x) and its inverse function are both plotted on the same coordinate plane, their point of intersection is (2,2).

What is inverse of a function?

Inverse function is represented by f-1 with regards to the original function f and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.

Intercept form of the given line:  $\frac{x}{3} + \frac{y}{6} =1$

Equation the line: $2x + y = 6$

Function becomes: $y = 6 - 2x\ or\ f(x) = -2x + 6$

Inverse of the function: $x = \frac{6-y}{2}\ or\ g(y) = \frac{6-y}{2} or g(x) = \frac{6-x}{2}$

Inverse function as a line: $2y +x = 6$

Calculating the intersection of the two lines using substitution:

$2x + y = 6\\\\y = 6 - 2x\\\\2y + x = 6\\\\2(6-2x) + x = 6\\\\12 - 4x + x = 6\\\\-3x = -6\\\\x = 2\\\\y = 6 - 2*2 = 2$

Learn more about inverse of a function here

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