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Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
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x
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=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
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Set-Builder Notation:
{
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The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
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−
∞
,
∞
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Set-Builder Notation:
{
y
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Determine the domain and range.
Domain:
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−
∞
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∞
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,
{
x
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x
∈
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}
Range:
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∞
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∞
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{
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y
∈
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}
The mean is 7.5 you add up all the numbers and then divide by the amount of numbers there is
I assume you're needing to find
given those two functions you have.
![\begin{aligned}(f+g)(x) &= f(x) + g(x) \\[0.5em] &= (5x^3+5x^2-6x+3) + (x^3-4x^2+x-2)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%28f%2Bg%29%28x%29%20%26%3D%20f%28x%29%20%2B%20g%28x%29%20%5C%5C%5B0.5em%5D%20%26%3D%20%285x%5E3%2B5x%5E2-6x%2B3%29%20%2B%20%28x%5E3-4x%5E2%2Bx-2%29%5Cend%7Baligned%7D)
From there, you combine like terms:
![\begin{aligned}(f+g)(x) &= f(x) + g(x) \\[0.5em] &= (5x^3+5x^2-6x+3) + (x^3-4x^2+x-2) \\[0.5em] &= 6x^3+x^2-5x+1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%28f%2Bg%29%28x%29%20%26%3D%20f%28x%29%20%2B%20g%28x%29%20%5C%5C%5B0.5em%5D%20%26%3D%20%285x%5E3%2B5x%5E2-6x%2B3%29%20%2B%20%28x%5E3-4x%5E2%2Bx-2%29%20%5C%5C%5B0.5em%5D%20%26%3D%206x%5E3%2Bx%5E2-5x%2B1%5Cend%7Baligned%7D)
Answer:
Divide both sides by 3.
(x+2)^2=16
Square root both sides.
x+2= ± 4 (plus OR minus, can be either so we have to include both)
Minus 2 from both sides.
x=-2 ± 4
Add and minus the 4 to -2.
x = -2-4 = -6 and x=-2+4 = 2