Question

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

Answer 1

Answer:

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.

Answer 2

The options are not shown, but you can see the graph in the image below.

Two functions f(x) and g(x) are inverses if the composite functions are equal to the identity.

This means that:

f(g(x)) = g(f(x)) = x.

Now, in this problem, we know that  f(x) and g(x) are inverse functions, and we want to find the graph of f(g(x)).

Using the above relation, we know that:

f(g(x)) = x

This is a really simple graph, and you can see it in the image below.

If you want to learn more, you can read:

https://brainly.com/question/10300045