If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))

The graph is attached; it is the graph of f(x) = x.

Step-by-step explanation:

Two functions are inverses if their composites form the function f(x) = x.

Take, for example, the function f(x) = 2x-4.  We can write this as y=2x-4.

To find the inverse, we isolate x.  To do this, first add 4 to each side:

y+4 = 2x-4+4

y+4 = 2x

Divide both sides by 2:

(y+4)/2 = 2x/2

y/2 + 4/2 = x

1/2y + 2 = x

Swap x and y, and the inverse is

y=1/2x+2

This can be written as g(x).

The composite of these two functions, f(g(x)), is:

f(1/2x+2) = 2(1/2x+2)-4

= 2(1/2x)+2(2)-4

=1x+4-4

= x

The composite of two functions is always f(x) = x.

This means the graph will have a slope of 1 and a y-intercept of 0.

step-by-step explanation:

the answer is 128

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