QuestionEvaluate $(g \circ f)(2)$ where $f(x)=x^{3}-7x$ and $g(x)=\sqrt{5x}$ .

Studdy Solution

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 $g(x)$ .
$g(-)=\sqrt{5 \cdot -}$

STEP 6

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.

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