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)

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AFOKE88 AFOKE88 · Answer 1 · 2022-08-26T17:50:44+02:00

Their point of intersection is (2,2)

The equation of f(x) is a line that passes through the points (0,6) and (3,0)

Find the slope. The slope is;

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

m = -2

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

f(x) = -2x + 6

Find the inverse;

Let y = f(x)

y = -2x + 6

Exchange the variables x for y and y for x and then Isolate the variable y

2y = -x + 6

y = -0.5x + 3

Let f⁻¹(x) = y

Thus;

f⁻¹(x) = -0.5x + 3

Solve the system of equations;

-0.5x + 3 = -2x + 6

Solving for x gives x = 2

Thus;

y = -0.5(2) + 3

y = 2

The solution is the point (2,2)

Thus, their point of intersection is (2,2)

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