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Fudgin [204]
3 years ago
13

F(x) = 3x^4 is even or odd?

Mathematics
2 answers:
tia_tia [17]3 years ago
8 0

Answer:

even function

Step-by-step explanation:

recall that:

a function is EVEN if and only if f(-x) = f(x) for all x in the domain of f

a function is ODD if and only if f(-x) = -f(x) for all x in the domain of f

we observe that for the function

f(x) = 3x^4

because x has been raised to an even power, that f(x) will always be positive (or zero), regardless of whether x is negative or positive.

i.e

f(x) = f(x)   and   f(-x) = f(x)

This behavior is described by the definition of an EVEN function (given above)

Hence f(x) is an even function

lara31 [8.8K]3 years ago
3 0

Answer:

Step-by-step explanation:

it's even because f(-x)=f(x)

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Write the simplest polynomial function with the given roots 2i, square root of 3, and 4
Volgvan

Answer:

  • y = (x - 4)(x + 2i)(x - 2i)(x + √3)(x - √3) Possible answer
  • y = (x - 4)(x^2 + 4)(x^2 - 3)                    Possible answer

Step-by-step explanation:

The simplest answer is that 2i cannot be a lone root. It must have a twin that is - 2i

√3 has the same sort of rule. It cannot be a root all by itself. It also must have a twin, in this case -√3

So the answer must be

(x - 4)(x + 2i)(x - 2i)(x + √3)(x - √3)      <<< Possible answer

but this can be reduced even further.

  • (x + 2i)(x - 2i) = x^2 - x*2i + x*2i - 4i^2
  • (x + 2i)(x - 2i) = x^2 - 4(i)^2
  • (x + 2i)(x - 2i) = x^2  + 4.               Remember i^2 = - 1

By a similar method (x - √3)(x + √3) = x^2 - 3

So the polynomial is reduced to

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

If this is not among your answers and the  factored form is not either, please tell me what is.

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Answer:

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Which linear equation could David use to determine y, the total distance he could swim without stopping to rest?
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Answer:

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Step-by-step explanation:

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Can someone please help me?
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