Find f(g(a)) f(a)=2a-1 g(a)=a-5

$f (a) = 2 a - 1$ $g (a) = a - 5$

Set up the composite result function.

$f (g (a))$

Evaluate $f (a - 5)$ by substituting in the value of $g$ into $f$ .

$f (a - 5) = 2 (a - 5) - 1$

Simplify each term.

Apply the distributive property.

$f (a - 5) = 2 a + 2 \cdot - 5 - 1$

Multiply $2$ by $- 5$ .

$f (a - 5) = 2 a - 10 - 1$

Subtract $1$ from $- 10$ .

$f (a - 5) = 2 a - 11$