Question

1.) evaluate: 3x + 2, when x = 5
2.) evaluate: -4y² + 7, when y = -1
3.) evaluate: 2x - y, when x = 4, y = 3
4.) evaluate: x² - 2xy + y², when x = 2, y = 5
5.) if f(x) = x² - 6x + 8, find: f(3)
6.) given g(x) = -2x² + 4x - 1, find: g(-1) and g(2)

Explanation:

Step1: Substitute $x=5$ into $3x+2$

$3(5) + 2$

Step2: Calculate the result

$15 + 2 = 17$

Step1: Substitute $y=-1$ into $-4y^2+7$

$-4(-1)^2 + 7$

Step2: Simplify the squared term

$-4(1) + 7$

Step3: Calculate the result

$-4 + 7 = 3$

Step1: Substitute $x=4,y=3$ into $2x-y$

$2(4) - 3$

Step2: Calculate the result

$8 - 3 = 5$

Step1: Substitute $x=2,y=5$ into $x^2-2xy+y^2$

$2^2 - 2(2)(5) + 5^2$

Step2: Simplify each term

$4 - 20 + 25$

Step3: Calculate the result

$4 - 20 + 25 = 9$

Step1: Substitute $x=3$ into $f(x)=x^2-6x+8$

$3^2 - 6(3) + 8$

Step2: Simplify each term

$9 - 18 + 8$

Step3: Calculate the result

$9 - 18 + 8 = -1$

Step1: Find $g(-1)$: substitute $x=-1$ into $g(x)=-2x^2+4x-1$

$-2(-1)^2 + 4(-1) - 1$

Step2: Simplify $g(-1)$

$-2(1) - 4 - 1 = -2 - 4 - 1 = -7$

Step3: Find $g(2)$: substitute $x=2$ into $g(x)=-2x^2+4x-1$

$-2(2)^2 + 4(2) - 1$

Step4: Simplify $g(2)$

$-2(4) + 8 - 1 = -8 + 8 - 1 = -1$

Answer:

1. $17$
2. $3$
3. $5$
4. $9$
5. $-1$
6. $g(-1)=-7$, $g(2)=-1$