Solve the Function Operation f(x) = square root of 3x-9 , g(x)=1/x , (f-g)(x)

$f (x) = \sqrt{3 x - 9}$ , $g (x) = \frac{1}{x}$ , $(f - g) (x)$

Step 1

Evaluate $f - g$ .

Replace the function designators in $f - g$ with the actual functions.

$(\sqrt{3 x - 9}) - (\frac{1}{x})$

Factor $3$ out of $3 x - 9$ .

Factor $3$ out of $3 x$ .

$\sqrt{3 (x) - 9} - (\frac{1}{x})$

Factor $3$ out of $- 9$ .

$\sqrt{3 x + 3 \cdot - 3} - (\frac{1}{x})$

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\sqrt{3 (x - 3)} - (\frac{1}{x})$

$\sqrt{3 (x - 3)} - \frac{1}{x}$

To write $\sqrt{3 (x - 3)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\sqrt{3 (x - 3)} x}{x} - \frac{1}{x}$

Combine the numerators over the common denominator.

$\frac{\sqrt{3 (x - 3)} x - 1}{x}$

Step 2

Evaluate $f - g$ at $x$ .

$\frac{\sqrt{3 ((x) - 3)} (x) - 1}{x}$

Step 3

Simplify $\frac{\sqrt{3 ((x) - 3)} (x) - 1}{x}$ .

Remove parentheses.

$\frac{\sqrt{3 ((x) - 3)} (x) - 1}{x}$

Remove parentheses.

$\frac{\sqrt{3 (x - 3)} x - 1}{x}$