If g(x) is the inverse of f(x), what is the value of f(g(2)?

Explanation:

g(x) is the inverse of f(x), which tells us that g undoes everything f(x) does.

If we input x = -6 then f(x) outputs 1

g(x) then reverses this to say that g(1) = -6. The inputs and outputs swap roles.

Moving to row 2, we see that f(-3) = 2 which reverses to g(2) = -3

We'll replace the g(2) with -3 to go from

f( g(2) )

to

f( -3 )

-3 isn't the answer, but I wanted to put it in bold to show how the replacement is happening.

From the table, we see that f(-3) = 2 which is the final answer

In other words, f(g(2)) = 2

Side note:

We can say that f(g(x)) = x for any number x in the domain of g(x).

As another example, g(3) = 5 and f(g(3)) = f(5) = 3.

The same works the other way around meaning that g(f(x)) = x.

C. 2

hope it helps :)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be