Algebra Examples

$f (x) = \sqrt{x - 1}$ , $g (x) = x^{2} - x$ , $(f - g) (10)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(\sqrt{x - 1}) - (x^{2} - x)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\sqrt{x - 1} - x^{2} - - x$

Step 1.2.2

Multiply $- - x$ .

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Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

$\sqrt{x - 1} - x^{2} + 1 x$

Step 1.2.2.2

Multiply $x$ by $1$ .

$\sqrt{x - 1} - x^{2} + x$

Step 1.3

Move $\sqrt{x - 1}$ .

$- x^{2} + x + \sqrt{x - 1}$

Step 2

Evaluate $f - g$ at $10$ .

$- {(10)}^{2} + 10 + \sqrt{(10) - 1}$

Step 3

Simplify $- {(10)}^{2} + 10 + \sqrt{(10) - 1}$ .

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Step 3.1

Remove parentheses.

$- {(10)}^{2} + 10 + \sqrt{(10) - 1}$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $10$ to the power of $2$ .

$- 1 \cdot 100 + 10 + \sqrt{(10) - 1}$

Step 3.2.2

Multiply $- 1$ by $100$ .

$- 100 + 10 + \sqrt{(10) - 1}$

Step 3.2.3

Subtract $1$ from $10$ .

$- 100 + 10 + \sqrt{9}$

Step 3.2.4

Rewrite $9$ as $3^{2}$ .

$- 100 + 10 + \sqrt{3^{2}}$

Step 3.2.5

Pull terms out from under the radical, assuming positive real numbers.

$- 100 + 10 + 3$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $- 100$ and $10$ .

$- 90 + 3$

Step 3.3.2

Add $- 90$ and $3$ .

$- 87$