I. Multiply the first function by the second one.
f(x)*g(x) = (x^2+3x-4)*(x+4) = x^3 + 3x^2 - 4x + 4x^2 + 12x -16 = x^3 +7x^2 + 8x - 16.
The domain of this new function is the set of all real numbers (R). Other notation: from minus infinity to plus infinity. We came to this conclusion because the new function poses no restrictions; regardless of which x-value you take, you will get the appropriate y-value.
II. f(x)/g(x) = (x^2+3x-4)/(x+4) =
Ask yourself: which two numbers add up to 3 and multiply to -4? It's -1 and 4. Now we can represent f(x) as (x-1)(x+4).
Since we're dividing these 2 brackets by g(x)=x+4, we may now cancel (x+4). All that's left is x-1.
The domain here is the same as in the previous task - it is R.
Maybe try searching it up cause I’m not exactly sure if my answers would be right
When something says 'solve for the system of equations' they are looking for a point where the graph of the two functions intersects. Since they give you the graph, the two functions approximately intersect somewhere between the x-value of -6 and -7 (i.e. -6.5) and somewhere between the y-value of -3 and -4 (i.e. -3.5). So, the closest estimate is (-6.5, -3.5) or A.
2x + 6 = 4x/2 + 12/2
To solve this, we need to transpose like terms to the same side.
2x - 4x/2 = 12/2 - 6
2x - 2x = 6 - 6
0 = 0
Since both sides are zero, it means that the equation has infinite number of solutions.
For
solving system of equations, we can use either substitution where we plug one
equation into the other, or elimination where we combine the equations.
-
Using elimination,
you would to eliminate one variable from both equations, so you automatically would
get one equation with one variable!
- Using
substitution
means you are going to solve one equation for one variable and substitute with
its value in the other equation in order to get also an equation with one
variable.
Let's take an example ...
y+x=2 and y-2x = 1
<span>Using <span>elimination, we need to subtract these two equation; one from the other...
y+x=2
-
y-2x=1
-----------
0+3x=1
then
x=1/3 and then substitute into any equation to get y-value</span></span>
y+x=2
y+1/3 = 2 >>>>>
y=5/3NOW...<span>Using substitution
</span>y+x=2 and y-2x = 1 >>(y=1+2x)
Plug (y=1+2x) into y+x=2 and solve for x
y+x=2
(1+2x) + x =2
1+3x = 2
3x=1
again (and for sure)
x = 1/3plug in x=1/3 into any of the equations above to get y:
y+x=2
y+1/3=2
y=5/3DOne !!!!!!
I hope you got
the idea
If you still need help, just let me know.