Algebra Examples

$f (x) = x - 2$ and $g (x) = x^{2} - 7 x - 9$ find $f (g (- 1))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} - 7 x - 9)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} - 7 x - 9) = (x^{2} - 7 x - 9) - 2$

Step 3

Subtract $2$ from $- 9$ .

$f (x^{2} - 7 x - 9) = x^{2} - 7 x - 11$

Step 4

Evaluate the result function by replacing $x$ with $- 1$ in the function.

${(- 1)}^{2} - 7 \cdot - 1 - 11$

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 $- 1$ to the power of $2$ .

$1 - 7 \cdot - 1 - 11$

Step 5.1.2

Multiply $- 7$ by $- 1$ .

$1 + 7 - 11$

Step 5.2

Simplify by adding and subtracting.

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Step 5.2.1

Add $1$ and $7$ .

$8 - 11$

Step 5.2.2

Subtract $11$ from $8$ .

$- 3$