what Is (g o f)(2)?

Question

what Is (g ^o f)(2)?

Answer 1

This is called a composition of functions, and it works kind of like a Russian nesting doll. Essentially, this function is asking you to plug the number 2 into the function f, then take that result and plug it into the function g.

Here is an example:

g(x) = 2x + 1

f(x) = 4x - 1

To solve (g o f)(2), first plug 2 into function f, then take your answer from that and plug it into function g.

f(2) = 4(2)-1 = 7

g(7) = 2(7) + 1 = 15

Therefore, (g o f)(2) = 15.

As a side note, there is a second way to solve these kind of problems. Take the entire function f , and plug it into the function g, then plug the number 2 in. Using the example from before:

g(x) = 2x + 1

f(x) = 4x - 1

(g o f)(x) = 2(4x-1) + 1 which simplifies to (g o f)(x) = 8x - 1. Now plug in the 2:

(g o f)(2) = 8(2) - 1 = 15

This method is useful if you will be using the composition of functions multiple times, such as (g o f)(1), (g o f)(2), etc. Note that since you haven't solved for x in function f, the x from that function remains an x when the entire function is plugged into function g. This complication is why I prefer the first method, as it can lead to silly mistakes when working with exponential functions.