The table below shows some values of the functions f and g for several integer values of x. | x | f(x) | g(x) | | :---: | :---: | :---: | | -2 | 3 | 1 | | -1 | 4 | -2 | | 0 | -1 | 3 | | 1 | 2 | 0 | | 2 | -2 | -1 | | 3 | 1 | 2 | What is the value of f(f(3)) + g(g(-1))?

The table below shows some values of the functions f and g for several integer values of x… — ACT

The table below shows some values of the functions $f$ and $g$ for several integer values of $x$ .

What is the value of $f(f(3)) + g(g(-1))$ ?

Answer: 3

The value of the expression is

3

To evaluate

f(f(3)) + g(g(-1))

, we start by evaluating the innermost expressions. Looking at the table for

x = 3

, we find

f(3) = 1

. Looking at the table for

x = -1

, we find

g(-1) = -2

. Substituting these values into the outer functions gives

f(1) + g(-2)

. Using the table again, we look up

x = 1

to find

f(1) = 2

, and look up

x = -2

to find

g(-2) = 1

. Adding these two results yields

2 + 1 = 3

Find the inner function values from the given table.

f(3) = 1

and

g(-1) = -2

Before evaluating the composite functions, we must find the outputs of the innermost functions.

Evaluate the outer functions using the results from the first step.

f(f(3)) = f(1) = 2

and

g(g(-1)) = g(-2) = 1

Substitute the inner outputs into the outer functions and look up the new inputs in the table.

Add the two resulting values together.

2 + 1 = 3

Combine the two terms to find the total sum requested by the question.

Evaluating composite functions using tables of values

Estimated Time:1m 0s