1.The domain of the function f(x)=20x/6x?1 is Write the answer in interval notat

Question

1.The domain of the function f(x)=20x/6x?1 is  
Write the answer in interval notation.

Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter ?? as -INF and ?as INF.
You might need to use brackets [ ] for closed intervals

2.The domain of the function f(x)=?13x+17/x^2?7x+10 is  
Write the answer in interval notation.
3.he domain of the function h(x)=1/x^2?7x???????4 is  
Write the answer in interval notation.

4.
The domain of the function 3x?18??????? is

The domain of the function ?3x?18???????? is

5.

Explanation / Answer

1.)  f(x)=20x/(6x-1)

=>f(x)=0

=>0 =20x/(6x-1)

only for x = 1/6

x can take any real number except 1/6 since x = 1/6 would make the denominator equal to zero and the division by zero is not allowed in mathematics. Hence the domain in interval notation is given by

hence domain s (-infinity,1/6)U(1/6,+infinity) or R - {1/6}

2)f(x)=13x+17/(x^2-7x+10) or f(x)=13x+(17/x^2)-7x+10

f(x)=13x+17/(x^2-7x+10) taking this as real function

f(x) is defined at all x R except where
x^2-7x+10 = 0

=>x=5,2

x^2-7x+10 factors as (x - 5)(x - 2), and (x - 5)(x - 2) is 0 exactly when x = 5 or x = 2.
Thus the domain of f is all real numbers except for 2 and 5. This can be
expressed as (-INF, 2) U (2, 5) U (5, INF) or as R - {2, 5}.

3) h(x)=1/(x^2-7x) or h(x)=(1/x^2)-7x

h(x)=1/(x^2-7x) taking this as real function

f(x) is defined at all x ? R except where
x^2-7x> 0

=>x>7

.
Thus the domain is(-INF,0) U(7, INF) same as 4

4) f(x)=sqrt(3x-18)

sqrt(3x-18)can never less zero. To do this, use an inequality. That is,

3x-18 > 0

Now just solve for x...

3x > 18

x > 6

This last inequality *is* the domain of the function. Try it. If x = -6, you get sqrt(0) = 0. This is ok. If x>-6(that is, less negative), you get the square root of a positive number. This is ok. If x is less than this number (more negative), you get the square root of a negative numbesqrt()of negative is not defined hence

hence domain is [6,INF)

5) f(x)=-3x-18

sqrt(-3x-18)can never less zero. To do this, use an inequality. That is,

-3x-18 > 0

Now just solve for x...

-3x > 18

x < -6

This last inequality *is* the domain of the function. Try it. If x = -6, you get sqrt(0) = 0. This is ok. If x<-6(that is, less negative), you get the square root of a positive number. This is ok. If x is less than this number (more negative), you get the square root of a negative numbesqrt()of negative is not defined hence

hence domain is (-INF,-6]

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.