Math Snap

STEP 1

What is this asking?
If we apply the function $f$ to the number $2$, we get $4$.
If we apply the function $g$ to the number $4$, we get $3$.
What do we get if we apply $g$ after applying $f$ to the number $2$?
Watch out!
Don't multiply the results of $f(2)$ and $g(4)$!
We need to apply $f$ first, then $g$ to the result.

STEP 2

1. Understand Function Composition
2. Evaluate the Composition

STEP 3

Function composition, denoted by $(g \circ f)(x)$, means applying $f$ to $x$ first, and then applying $g$ to the result.
Think of it like a chain reaction!

STEP 4

In our case, $(g \circ f)(2)$ means we first find $f(2)$, and then we plug that result into $g$.

STEP 5

We are given that $f(2) = 4$.
This means when we plug $2$ into $f$, we get $4$.
This is our intermediate result.

STEP 6

Next, we need to find $g(f(2))$, which is the same as $g(4)$ since $f(2) = 4$.

STEP 7

We are given that $g(4) = 3$.
So, when we plug $4$ into $g$, we get $3$.
This is our final result!

The answer is (c) $3$.