Math Snap

STEP 1

What is this asking?
We're given two functions, $f(x) = \sqrt{x}$ and $g(x) = x^2 - 4$, and we need to find $g(3)$ and then use that result to find $f(g(3))$.
Watch out!
Make sure to apply the functions in the correct order!
We need $g(3)$ first, then we plug that result into $f(x)$.
Also, remember the order of operations when evaluating $g(3)$.

STEP 2

1. Evaluate $g(3)$
2. Evaluate $f(g(3))$

STEP 3

We're given the function $g(x) = x^2 - 4$.
To find $g(3)$, we substitute $x = 3$ into the function:
$$g(3) = (3)^2 - 4$$

STEP 4

Now, let's calculate the result!
First, we square the 3:
$$g(3) = 9 - 4$$ Then, we subtract 4 from 9:
$$g(3) = 5$$ So, $g(3) = \textbf{5}$!

STEP 5

We just found that $g(3) = \textbf{5}$.
Now, we need to find $f(g(3))$, which is the same as finding $f(5)$ since $g(3)$ is 5.

STEP 6

Our function $f(x)$ is defined as $f(x) = \sqrt{x}$.
We substitute our value of 5 for $x$:
$$f(5) = \sqrt{5}$$

STEP 7

Now, we calculate the square root of 5:
$$f(5) \approx 2.236$$ Rounding to two decimal places, we get $\textbf{2.24}$.

Part 1: $g(3) = 5$
Part 2: $f(g(3)) = 2.24$