QuestionFind the graph of $(f-g)(x)$ where $f(x)=\frac{1}{x}$ and $g(x)=\sqrt{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=\frac{1}{x}$ . The function $g(x)=\sqrt{x}$
3. We are asked to find the graph of $(f-g)(x)$

STEP 2

First, we need to find the expression for $(f-g)(x)$ . This is done by subtracting the function $g(x)$ from $f(x)$ .
$(f-g)(x) = f(x) - g(x)$

STEP 3

Now, plug in the given functions for $f(x)$ and $g(x)$ to calculate $(f-g)(x)$ .
$(f-g)(x) = \frac{1}{x} - \sqrt{x}$

STEP 4

This is the expression for $(f-g)(x)$ . To graph it, we need to plot this function.It's important to note that the domain of this function is $x >0$ , because we have a square root function (which is undefined for negative numbers) and a reciprocal function (which is undefined for zero).

STEP 5

Now, we can plot the function $(f-g)(x) = \frac{1}{x} - \sqrt{x}$ for $x >0$ .
Unfortunately, as an AI, I can't physically draw the graph. However, I can tell you that the graph starts at a high positive value for small $x$ , decreases rapidly, crosses the x-axis at $x=1$ , and then becomes negative and decreases slowly for larger $x$ .

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