Find f(g(x)) f(x)=5x-2 , g(x)=-x^2+4x-1

$f (x) = 5 x - 2$ , $g (x) = - x^{2} + 4 x - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- x^{2} + 4 x - 1)$ by substituting in the value of $g$ into $f$ .

$f (- x^{2} + 4 x - 1) = 5 (- x^{2} + 4 x - 1) - 2$

Step 3

Simplify each term.

Apply the distributive property.

$f (- x^{2} + 4 x - 1) = 5 (- x^{2}) + 5 (4 x) + 5 \cdot - 1 - 2$

Simplify.

Multiply $- 1$ by $5$ .

$f (- x^{2} + 4 x - 1) = - 5 x^{2} + 5 (4 x) + 5 \cdot - 1 - 2$

Multiply $4$ by $5$ .

$f (- x^{2} + 4 x - 1) = - 5 x^{2} + 20 x + 5 \cdot - 1 - 2$

Multiply $5$ by $- 1$ .

$f (- x^{2} + 4 x - 1) = - 5 x^{2} + 20 x - 5 - 2$

Step 4

Subtract $2$ from $- 5$ .

$f (- x^{2} + 4 x - 1) = - 5 x^{2} + 20 x - 7$