What is the domain of the functions below:
y= 2x−3/|x-1|+2
assuming you mean what you typed:
y= 2x−3/|x-1|+2
when x = +1 the denominator is zero so it is all real x except x = 1
if you meant
y= 2x−3/ (|x-1|+2 )
the denominator is always positive so the domain is all real x
thanks:)
To determine the domain of the given function, we need to consider values of x that make the function undefined.
The function contains an absolute value expression in the denominator, specifically |x-1|. Absolute value expressions are defined for all real numbers except when the expression inside the absolute value is equal to zero. In this case, x-1 cannot be equal to zero because it would result in division by zero.
So, we need to find the values of x that make x-1 equal to zero:
x - 1 = 0
x = 1
Thus, x cannot equal 1 because it would result in division by zero. Therefore, the domain of the function y = (2x - 3) / |x - 1| + 2 is all real numbers except x = 1. In interval notation, the domain can be expressed as (-∞, 1) U (1, ∞).