Precalculus Examples

$f (x) = x^{2} + 1$ $g (x) = 2 x - 5$ Find $f (x) - g (x)$

Step 1

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

$(x^{2} + 1) - (2 x - 5)$

Step 2

Simplify $(x^{2} + 1) - (2 x - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x^{2} + 1 - (2 x) - - 5$

Step 2.1.2

Multiply $2$ by $- 1$ .

$x^{2} + 1 - 2 x - - 5$

Step 2.1.3

Multiply $- 1$ by $- 5$ .

$x^{2} + 1 - 2 x + 5$

Step 2.2

Add $1$ and $5$ .

$x^{2} - 2 x + 6$