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Katarina [22]
3 years ago
14

Prove algebraically what type of function this is (even, odd, or neither).f(x) = x^6 – x^4​

Mathematics
1 answer:
Savatey [412]3 years ago
3 0

Let's see.

We have function f(x)=x^6-x^4. We have to determine if the function is even or odd or neither.

We can find this out in many ways but the assignment specifically asks to prove this algebraically.

Function is even if f(x)=f(-x), so, x^6-x^4=(-x)^6-(-x)^4

Which is true since negative raised to an even power is positive to that same number.

Similarly, function is odd if f(x)=-f(-x), that is,

x^6-x^4\neq-((-x)^6-(-x)^4).

So we have prooved that function f(x) is an even function not an odd function and therefore also not neither.

Hope this helps.

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John is about to roll a six sided, fair number cube 60
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Answer:

No it is not a good prediction. Theoretical probability says that the answer would be 30 of the 60 (30/60) rolls would be even numbers.

Step-by-step explanation:

The probability of rolling an even number on a fair six sided die is 3/6 or 1/2 when simplified.

if john rolls the die 60 times, multiply the theoretical probability (1/2) by the number of rolls

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∴ theoretical probability says that john would roll an even number 30 out of the 60 rolls

I hope this was helpful :-)

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Jacob is 5 5/6 feet tall. Linda is 5 1/4 feet tall. How much taller is Jacob?
SCORPION-xisa [38]
This problem boils down to 5/6 - 1/4

To subtract these fractions you need a common denominator.

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So Jacob is 7/12 of a foot taller than Linda.

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