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3 years ago

Please help ASAP 25 pts + brainliest to right/best answer

Mathematics

2 answers:

Sladkaya [172]3 years ago

8 0

Step-by-step

This problem is asking us to multiply f(x) and g(x).

{f(x)}{g(x)} = (2x^2 + x - 3)(x - 1)

Use the Distributive Property of Multiplication to multiply the functions.

(2x^2)(x) + (2x^2)(-1) + (x)(x) + (x)(-1) + (-3)(x) + (-3)(-1)

Simplify

(2x^3) + (-2x^2) + (x^2) + (-x) + (-3x) + (3)

Combine like terms

2x^3 + (-x^2) + (-4x) + 3

Answer

(a) 2x^3 - x^2 - 4x + 3

Marina86 [1]3 years ago

7 0

Answer:

Step-by-step explanation:

This is my other account so i can mark you brainliest

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3 years ago

Please help me! Find the number x such that f(x) =1

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Answer:

Step-by-step explanation:

We have the piecewise function:

$f(x) = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

And we want to find x such that f(x)=1.

So, let's substitute 1 for f(x):

$1 = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

This has two equations. So, we can separate them into two separate cases. Namely:

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Let's solve for x in each case.

Case I:

We have:

$1=-\frac{1}{2}x-1$

Add 1 to both sides:

$2=-\frac{1}{2}x$

Let's cancel out the fraction by multiplying both sides by -2. So:

$2(-2)=(-2)\frac{-1}{2}x$

The right side cancels:

$-4=x\\$

Flip:

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So, x is -4.

Case II:

We have:

$1=x$

Flip:

$x=1$

This is the solution for our second case.

So, we have:

$x_1=-4\text{ or } x_2=1$

Now, can check to see if we have to to remove solution(s) that don't work.

Note that x=-4 is the solution to our first equation.

The first equation is defined only if x is less than -2.

-4 is less than -2. So, x=-4 is indeed a solution.

x=1 is the solution to our second equation.

The second equation is defined only if x is greater than or equal to -2.

1 is greater than or equal to -2. So, x=1 is also a solution.

Therefore, our two solutions are:

$x_1=-4\text{ or } x_2=1$

Out of our answer choices, we can pick D.

And we're done!

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