Math Snap

STEP 1

Assumptions1. We have three functions $f(x)=x^{3}-7 x$, $g(x)=\sqrt{5 x}$, and $h(x)= x-5$.
. We need to evaluate the function $(g \circ f)(x)$ for $x=$.
3. The notation $(g \circ f)(x)$ means that we first apply the function $f$ to $x$, and then apply the function $g$ to the result.

STEP 2

First, we need to evaluate the function $f(x)$ at $x=2$. This is done by substituting $x=2$ into the function $f(x)$.
$$f(2)=2^{}-7 \cdot2$$

STEP 3

Calculate the value of $f(2)$.
$$f(2)=2^{3}-7 \cdot2 =8 -14 = -6$$

STEP 4

Now that we have the value of $f(2)$, we can substitute this value into the function $g(x)$ to evaluate $(g \circ f)(2)$.
$$g(f(2))=g(-6)$$

STEP 5

Substitute $x=-$ into the function $g(x)$.
$$g(-)=\sqrt{5 \cdot -}$$

Calculate the value of $g(-6)$.
Since the square root of a negative number is not a real number, $g(-6)$ is undefined in the real number system. Therefore, $(g \circ f)(2)$ is also undefined.
$(g \circ f)(2)$ is undefined.