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3 years ago

Find the domain of the function:

Mathematics

2 answers:

makkiz [27]3 years ago

8 0

Answer: OPTION C.

Step-by-step explanation:

1. The domain of the function given in the problem are all those values for which the function that is in the denomiantor is different from zero, because the division by 0 is not allowed.

2. You can make the denominator equal to zero and solve it, as you can see below:

$x^{3}-2x^{2}+x=0\\x(x^{2}-2x+1)=0\\x(x-1)(x-1)=0\\x=0\\x=1$

3. Therefore, the domain is:

(-∞,0)U(0,1)U(1,∞)

ANEK [815]3 years ago

3 0

Answer:

Option C is correct.

Step-by-step explanation:

We have given the function.

f(x) = (x-1)²/(x³-2x²+x)

We have to find the domain of given function.

domain of function is all possible values of independent variable for which the function is difined.

So for this the denominator must not be zero.

x³-2x²+x ≠ 0

x(x²-2x+1)≠ 0

x(x-1)(x-1) ≠ 0

x ≠0 and x≠1

So, the domain cannot consist of x=0 and x=1.

Therefore, the domain is :

(-∞ , 0) ∪ (0,1 ) ∪ (1,+∞).

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QUESTION 10

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QUESTION 11

Sam divided the square backyard into two sections along the 40ft diagonal.

Let one of the sides of the garden be $x\:units$ , then the other side of the garden is also $x\:units$ since it was a square backyard.

The diagonal is the hypotenuse which is 40ft and the two legs are $x\:units$ each.

Applying the Pythagoras Theorem, we have;

$x^2+x^2=40^2$

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QUESTION 12

The hypotenuse of Nicole's right triangular support is 92cm long.

It was given that the two lengths of the triangular support are of equal length.

Let the two lengths of the triangular support be $l\:cm$ each.

We then apply the Pythagoras theorem to obtain;

$l^2+l^2=92^2$

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Therefore Nicole needs $l+l=65.05cm+65.05cm\approx130cm$ of wood to complete the support.

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Applying the Pythagoras Theorem, we have;

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3 years ago