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