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 :)

77

step-by-step explanation:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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