1. Simultaneous Solving of Equations

Ok so to simultaneously solve these to find the domains, I have done the first one. Would the rest be the exact same? How would I do the thrid and fourth one?

2. Re: Simultaneous Solving of Equations

When finding the domain of a function, you want to exclude those values of x which cause the function to be undefined (division by zero) or have complex values (an even root of a negative value). There are also restrictions on logarithmic and inverse trigonometric functions as well.

Polynomial functions such as the first two, have no restrictions on the domain as there is no division or radicals. For the remaining three, set the expressions under the radicals greater than or equal to zero, and solve for x. This will tell you the valid values for x, which is the domain of the function. What do you find?

3. Re: Simultaneous Solving of Equations

How do you set the expressions under the radical greater than or equal to 0?

4. Re: Simultaneous Solving of Equations

Just take the expression under the radical, and state that it is greater than or equal to zero. For example, doing this for the third one gives:

$\displaystyle x-60\ge0$

Now add 60 to both sides, and what does this tell you about $\displaystyle x$?

5. Re: Simultaneous Solving of Equations

that x is bigger than or equal to 60

6. Re: Simultaneous Solving of Equations

Yes, very good! Now how would you state this in the form:

$\displaystyle a\le x\le b$ ?

7. Re: Simultaneous Solving of Equations

so a would be 60, and how would you find b?

8. Re: Simultaneous Solving of Equations

Yes, good...is there any real number that x must be smaller in comparison? In other words, is there an upper bound for x?

9. Re: Simultaneous Solving of Equations

Yeah there has to be, but how do I figure that one out for the third and fourth?

10. Re: Simultaneous Solving of Equations

No, there is no upper bound so we use $\displaystyle \infty$ as the upper bound. So for the third one you would write:

$\displaystyle 60\le x\le\infty$

What did you write for the first two since there is no lower or upper bounds?