evaluating composite functions

Question

Given functions f(x) = 3x + 4 and g(x) = x² − 2, what is the value of f(g(−3))?

F. −29

G. −27

H. −20

J. 23

K. 25

Answer 1

Question: Given functions f(x) = 3x + 4 and g(x) = x² − 2, what is the value of f(g(−3))?

When it comes to composite functions, the simple rule is "inside function first, the work toward the outside function"

By this, I mean that you start with solving/simplifying the innermost function in the composite and use the sequential solution(s) to get to the final answer.

So if g(x) = x²-2 , then g(-3), the inner most function in the composite, is the same as this but you replace all of the x's with (-3).

if g(x) = x²-2, then g(-3) = (-3)²-2 = 9-2 = 7

now you just use this answer, 7, as a replacement for g(-3) in the composite function. This is the next most outer function in the composite function and the final one to get the final answer.

f(g(x)) = f(7)

So if f(x)= 3x + 4, then f(7) = 3(7) + 4 = 21 + 4 = 25

Final answer:

f(g(-3)) = f(7) = 25

Hope this helps.

Answer 2

In composite functions the output of the inner function becomes the input of the outer function.

In f(g(-3)), we will evaluate g(-3) first.

g(x) = x^2 -2. g(-3) = (-3)^2-2 = 9-2 7.

f(x) = 3x + 4. f(7) = 3(7) + 4. 21 -+ 4= 25.

So f(g(-3)) is 25.

Answer : K

Answer 3

"Function Composition" is applying one function to the results of another. When we are evaluating a composition of functions we start with the inside most function and work our way outward.

*In this case, we will evaluate g(-3) first. In the function named g(x) we will replace x with -3 and simplify.

g(-3) = (-3)² - 2 = 9 - 2 = 7

A Common error is confusing (-3)² = 9 with -3² = -9. Using parentheses () helps when substituting values for x

**Next, we replace g(-3) with 7 and evaluate the f(x) function when x= 7.

f(g-3)) = f(7) = 3(7) + 4 = 21 + 4 = 25

***The answer to this problem is 25