Question

In: Math

Explain how to solve the following problems step by step, andreason it should be solved...

Explain how to solve the following problems step by step, and reason it should be solved that way:

1) Find domain for each problem and explain in brief in each case. How do you find the domain of these problems without using a graph (don't state the problem only)?  Explain this: why is there a difference between in the domain of an even and an odd indexed radical? Why the domain of a function with a square root in the denominator IS different than the domain of a function with square root NOT in the denominator?

3 = a) c) *)=x2 + 7 f(x) =_ * +1 f(x) = 2247 f(x) = (x+7) x2 – 3x - 18 f(x) =


Solutions

Expert Solution

A rational function of the form

Is defined for every x except Q(x)=0. (denominator equal to zero)

So find x which corresponding to Q(x)=0. Then domain is all real number except this number.

A square root funtion

Is defined for every x except p(x) <0

So p(x) should be greater than or equal to 0.

Find x to which p(x)> 0 . This is domain.

a)

Here Q(x) is x2+7 .

x2+7=0

X2= -7

This is not possible for any real number . So domain is entire real number .

b).

Here Q(x) is x2-3x-18

x2-3x -18=0

For a quadratic equation ax2+bx+c=0

Here a=1 ,b= -3 ,c= -18

So

. Or.

So domain is all number except x=6 and x= -3

C)

Domain of a cube root funtion is all x .

So domain of

Is all x.

d)

This is rational function with square root funtion.

For square root funtion p(x)= 7-2x

P(x) should be greater than or equal to zero.

P(x)≥0

7-2x ≥0

Add 2x at both side . This will not effect the inequality.

7-2x+2x ≥0+2x

7≥2x

Divide both side by 2

3.5 ≥ x

So domain is all x less than 3.5 , including 3.5

Now consider condition for rational funtion.

Here

So funtion is defined for every x except

7-2x=0

2x=7

x=7/2=3.5

So funtion is not defined at x=3.5

So combining this two domain is all x less than 3.5

Domain of odd indexed radicle is all x.

Domain of even indexed radicle is only posative number.

For even

(-1)2= 12 =1

For odd indexed

(-1)3≠ 13

They are different.


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