Consider the functions f(x) = x2 − 13 and g(x) = x + 5. what is the value of f[g(−4)]? −12 3 −13 8

The value of that composite function is -12.

In order to solve for any value within a composite function, we first take the number and function on the innermost part and ignore the outermost part. In this case, we start with just g(-4). This means we stick -4 in for x in the g equation. The work for this is below.

g(x) = x + 5

g(-4) = -4 + 5

g(-4) = 1

Now that we have this, we use the answer (in this case 1) and put it into the outermost equation. So we are looking for f(1), which means we stick 1 in for x in the f equation.

f(x) = x^2 - 13

f(1) = 1^2 - 13

f(1) = 1 - 13

f(1) = -12

thus, the first answer choice, y = sec x, is the correct one