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morpeh [17]
3 years ago
6

Can someone please help me with this question?? It’s really hard and once you understand it, can you please give me an explanati

on? Thanks so much!!
( number:7)

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
3 0

We want to subtract 8x + 3 from -2x+5. We can create an expression to represent this.

-2x + 5 - (8x + 3).


After this, lets distribute the - sign (think of this like expanding something with -1).

-2x + 5 - 8x - 3


Lastly, we just need to combine like terms.

-2x + 5 - 8x - 3


Combine the 5 and -3 to get 2.

-2x + 2 - 8x


Combine the -2x and -8x to get -10x.

-10x + 2


The final answer to the question is therefore A.

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Answer:

1) (f+g)(x)=2x^2+3x-6

2) (f-g)(x)=2x^2+x

3) (f \cdot g)(x)=2x^3-4x^2-9x+9

Step-by-step explanation:

So we have the two functions:

f(x)=2x^2+2x-3\text{ and } g(x)=x-3

And we want to find (f+g)(x), (f-g)(x), and (f*g)(x).

1)

(f+g)(x) is the same to f(x)+g(x). Substitute:

(f+g)(x)=f(x)+g(x)\\=(2x^2+2x-3)+(x-3)

Combine like terms:

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So:

(f+g)(x)=2x^2+3x-6

2)

(f-g)(x) is the same to f(x)-g(x). So:

(f-g)(x)=f(x)-g(x)\\=(2x^2+2x-3)-(x-3)

Distribute:

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

Combine like terms:

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

Simplify:

=2x^2+x

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3)

(f*g)(x) is the same to f(x)*g(x). Thus:

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Distribute:

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Distribute:

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Combine like terms:

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Simplify:

=2x^3-4x^2-9x+9

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(f \cdot g)(x)=2x^3-4x^2-9x+9

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