Given sx 3x 6 and tx 6 3x find the simplified formula and domain for and
What is the simplified formula for and ?
The simplified formula for and is . The domain for this function is .
What is the domain for and ?
The domain for and is all real numbers.
How to find the simplified formula and domain for and
and can be simplified by factoring out the greatest common factor of 3. This leaves us with . The domain of is all real numbers.
Method 1: algebraic manipulation
In this method, we will use algebraic methods to find the simplified formula for and . We will also find the domain of .
First, let’s write out the equation for and :
We can see that in order to simplify this equation, we need to find a common denominator. In this case, the common denominator is . So, we need to multiply both the numerator and denominator of the first term by 3, and multiply both the numerator and denominator of the second term by 2:
= (sx * 3) / (tx * 3) – (6 * 2) / (tx * 2)
= (3sx) / (3tx) – 12 / (2tx)
= sx / tx – 6 / tx
Method 2: using the graph of the function
In order to find the domain and range of a function algebraically, you need to have the function in its simplest form. In some cases, it may be easier to find the domain and range by looking at the graph of the function.
To find the domain of a function graphically, look for any points where the function is undefined. In this case, the function is undefined when x = –2 or when x = 3. This means that the domain of the function is all values of x except –2 and 3.
To find the range of a function graphically, look for any points where the y-value is equal to or less than 0. In this case, there are no such points, so the range of the function is all positive values of y.
Thus, we can conclude that the simplified formula for and is and the domain for and is .