Find f(g(x)) f(x)=-2x-7 , g(x)=-4x+3

$f (x) = - 2 x - 7$ , $g (x) = - 4 x + 3$

Set up the composite result function.

$f (g (x))$

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

$f (- 4 x + 3) = - 2 (- 4 x + 3) - 7$

Simplify each term.

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Apply the distributive property.

$f (- 4 x + 3) = - 2 (- 4 x) - 2 \cdot 3 - 7$

Multiply $- 4$ by $- 2$ .

$f (- 4 x + 3) = 8 x - 2 \cdot 3 - 7$

Multiply $- 2$ by $3$ .

$f (- 4 x + 3) = 8 x - 6 - 7$

Subtract $7$ from $- 6$ .

$f (- 4 x + 3) = 8 x - 13$

Find f(g(x)) f(x)=-2x-7 , g(x)=-4x+3

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