Solve the Function Operation f(x)=x-2 and g(x)=x^2-7x-9 find f(g(-1))

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

Set up the composite result function.

$f (g (x))$

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

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

Subtract $2$ from $- 9$ .

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

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

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

Simplify the evaluated function.

Simplify each term.

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

$1 - 7 \cdot - 1 - 11$

Multiply $- 7$ by $- 1$ .

$1 + 7 - 11$

Simplify by adding and subtracting.

Add $1$ and $7$ .

$8 - 11$

Subtract $11$ from $8$ .

$- 3$