Question

3A. Explain in your own words how to find the domain of a function if you know its equation.B. Find the domain of f (x) =√9-7x6x?+13x-15Be sure to show relevant work.

Answer 1

Solution

Step 1

A)The domain refers to all real values of x for which the function is defined. The values of x for which the function is undefined are not a part of the domain. If you are given the equation then you can find the domain of that function by solving/ factorizing the denominator of the equation to find the zero(s) of the equation in the denominator. These values gotten are the values of x that will make the function undefined and hence are not part of the domain. Every other real value of x apart from these zero(s) obtained is part of the domain.

B)

Step 1

Factorize the denominator of the equation to find the zeroes of the equation

$6x^2+13x-15=0$

Step 2

Find the required factors to replace 13x and is equal to -90x²

$\text{These factors are 18x and -5x}$

Step3

Replace 13x with these factors

$6x^2+18x-5x-15=0$

Step 4

Factorize the equation and find the values of x

$\begin{gathered} (6x^2+18x)(-5x-15)=0 \\ 6x(x+3)\text{ -5(x+3)=0} \\ (6x-5)(x+3)=0 \\ 6x-5\text{ = 0} \\ 6x=5 \\ x=\frac{5}{6}\text{ OR} \\ x+3=0 \\ x=-3 \end{gathered}$

Hence, the domain of the function is all real values of x except -3 and 5/6