Finite Math Examples

$f (x) = x^{2} + 1$ , $g (x) = 1 - x^{2}$

Step 1

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

$x^{2} + 1 - (1 - x^{2})$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- 1$ by $1$ .

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

Step 2.3

Multiply $- - x^{2}$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

Multiply $x^{2}$ by $1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $x^{2} + 1 - 1 + x^{2}$ .

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Step 3.1.1

Subtract $1$ from $1$ .

$x^{2} + 0 + x^{2}$

Step 3.1.2

Add $x^{2}$ and $0$ .

$x^{2} + x^{2}$

Step 3.2

Add $x^{2}$ and $x^{2}$ .

$2 x^{2}$