Find f(g(x)) f(x)=-5x-4 and g(x)=6x-7

$f (x) = - 5 x - 4$ and $g (x) = 6 x - 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (6 x - 7)$ by substituting in the value of $g$ into $f$ .

$f (6 x - 7) = - 5 (6 x - 7) - 4$

Step 3

Simplify each term.

Apply the distributive property.

$f (6 x - 7) = - 5 (6 x) - 5 \cdot - 7 - 4$

Multiply $6$ by $- 5$ .

$f (6 x - 7) = - 30 x - 5 \cdot - 7 - 4$

Multiply $- 5$ by $- 7$ .

$f (6 x - 7) = - 30 x + 35 - 4$

Step 4

Subtract $4$ from $35$ .

$f (6 x - 7) = - 30 x + 31$