Precalculus Examples

$g (n) = n + 1$ $f (n) = n^{2} - n$ Find $g (f (8))$

Step 1

Set up the composite result function.

$g (f (n))$

Step 2

Evaluate $g (n^{2} - n)$ by substituting in the value of $f$ into $g$ .

$g (n^{2} - n) = (n^{2} - n) + 1$

Step 3

Remove parentheses.

$g (n^{2} - n) = n^{2} - n + 1$

Step 4

Evaluate the result function by replacing $n$ with $8$ in the function.

${(8)}^{2} - (8) + 1$

Step 5

Simplify the evaluated function.

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Step 5.1

Simplify each term.

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Step 5.1.1

Raise $8$ to the power of $2$ .

$64 - (8) + 1$

Step 5.1.2

Multiply $- 1$ by $8$ .

$64 - 8 + 1$

Step 5.2

Simplify by adding and subtracting.

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Step 5.2.1

Subtract $8$ from $64$ .

$56 + 1$

Step 5.2.2

Add $56$ and $1$ .

$57$