Can I please get some help with this homework problem?
The domain of a function refers to the input or x-values that will give you a real number for the value of the function. Cases that will not give a real value would include a 0 in the denominator or a negative value under the radical sign.
What is the domain of this function? (in interval notation)
f(x)=(x+20)/(x^2-16)
The denominator of this equation is x^2 - 16. Any value of x that will cause the denominator to become zero should be excluded from the domain. So set the denominator equal to zero and solve for x.
x^2 - 16 = 0
x^2 = 16
x = +/- 4
The domain of your function would be: All real numbers not equal to 4 or -4.
What is the domain of this function? (in interval notation)
f(x)=sqrt(2x-2)
The domain for this function can be determined by setting 2x - 2 </= to 0.
2x - 2 </= 0
2x </= 2
x </= 1
If x = 1, the number under the radical sign is 0. The sqrt(0) = 0, which is a real number. Any value of x less than 1 will result in a negative value under the radical sign, which will not give a real number answer.
The domain for this function: All real numbers less than or equal to 1.
