Determine the domain of each of the following functions. Write your answer for the domain in interval notation.

Question

f(x)=3x-1

f(x)= -1/x^2+2x-3

f(x)=Square root of x-6

Answer 1

a) this is in the form y=mx+b so is a line and is therefore deifened for all values of x.

 

b)-1/(x²+2x-3) is a rational function, or a fraction. When dealing with a fraction, the denominator cannot be 0. 

This means that x²+2x - 3 cannot equal 0.

(x+3)(x-1) cannot = 0

x cannot equal -3 and x cannot = 1.

 

c) with radical equations, the expression underneath the square root sign must be greater than or equal to 0 since the square root of negative numbers lead to imaginary numbers.

So, x-6 >=0 leads to x>=6.

 

Hope this helped.