Find f(g(x)) f(x)=4x^2+5x+6 , g(x)=5x-3

$f (x) = 4 x^{2} + 5 x + 6$ , $g (x) = 5 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x - 3)$ by substituting in the value of $g$ into $f$ .

$f (5 x - 3) = 4 {(5 x - 3)}^{2} + 5 (5 x - 3) + 6$

Step 3

Simplify each term.

Rewrite ${(5 x - 3)}^{2}$ as $(5 x - 3) (5 x - 3)$ .

$f (5 x - 3) = 4 ((5 x - 3) (5 x - 3)) + 5 (5 x - 3) + 6$

Expand $(5 x - 3) (5 x - 3)$ using the FOIL Method.

Apply the distributive property.

$f (5 x - 3) = 4 (5 x (5 x - 3) - 3 (5 x - 3)) + 5 (5 x - 3) + 6$

Apply the distributive property.

$f (5 x - 3) = 4 (5 x (5 x) + 5 x \cdot - 3 - 3 (5 x - 3)) + 5 (5 x - 3) + 6$

Apply the distributive property.

$f (5 x - 3) = 4 (5 x (5 x) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (5 x - 3) = 4 (5 \cdot (5 x \cdot x) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$f (5 x - 3) = 4 (5 \cdot (5 (x \cdot x)) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $x$ by $x$ .

$f (5 x - 3) = 4 (5 \cdot (5 x^{2}) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $5$ by $5$ .

$f (5 x - 3) = 4 (25 x^{2} + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $- 3$ by $5$ .

$f (5 x - 3) = 4 (25 x^{2} - 15 x - 3 (5 x) - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $5$ by $- 3$ .

$f (5 x - 3) = 4 (25 x^{2} - 15 x - 15 x - 3 \cdot - 3) + 5 (5 x - 3) + 6$

Multiply $- 3$ by $- 3$ .

$f (5 x - 3) = 4 (25 x^{2} - 15 x - 15 x + 9) + 5 (5 x - 3) + 6$

Subtract $15 x$ from $- 15 x$ .

$f (5 x - 3) = 4 (25 x^{2} - 30 x + 9) + 5 (5 x - 3) + 6$

Apply the distributive property.

$f (5 x - 3) = 4 (25 x^{2}) + 4 (- 30 x) + 4 \cdot 9 + 5 (5 x - 3) + 6$

Simplify.

Multiply $25$ by $4$ .

$f (5 x - 3) = 100 x^{2} + 4 (- 30 x) + 4 \cdot 9 + 5 (5 x - 3) + 6$

Multiply $- 30$ by $4$ .

$f (5 x - 3) = 100 x^{2} - 120 x + 4 \cdot 9 + 5 (5 x - 3) + 6$

Multiply $4$ by $9$ .

$f (5 x - 3) = 100 x^{2} - 120 x + 36 + 5 (5 x - 3) + 6$

Apply the distributive property.

$f (5 x - 3) = 100 x^{2} - 120 x + 36 + 5 (5 x) + 5 \cdot - 3 + 6$

Multiply $5$ by $5$ .

$f (5 x - 3) = 100 x^{2} - 120 x + 36 + 25 x + 5 \cdot - 3 + 6$

Multiply $5$ by $- 3$ .

$f (5 x - 3) = 100 x^{2} - 120 x + 36 + 25 x - 15 + 6$

Step 4

Simplify by adding terms.

Add $- 120 x$ and $25 x$ .

$f (5 x - 3) = 100 x^{2} - 95 x + 36 - 15 + 6$

Simplify by adding and subtracting.

Subtract $15$ from $36$ .

$f (5 x - 3) = 100 x^{2} - 95 x + 21 + 6$

Add $21$ and $6$ .

$f (5 x - 3) = 100 x^{2} - 95 x + 27$

Find f(g(x)) f(x)=4x^2+5x+6 , g(x)=5x-3

Related Questions

Support LCMGCF.com by disabling your adblocker.