How do you find the domain and range of #f (x) = 1 / ( x - 1)#?

Question

Kennedy Adams · Accepted Answer

Domain: all Real values excluding #1#
Range: all Real values excluding #0# Given #f(x)=1/(x-1)# Since division by #0# is undefined #color(white)("XXX")x-1 != 0# #color(white)("XXX")rarr x != 1# However #f(x)# is defined for all other values of #x# Since #f(x)=1/(x-1)# then #color(white)("XXX")(x-1)*f(x)=1# and the question of "Range" becomes #color(white)("XXX")#for what value(s) of #f(x)# is this not possible. The only answer is that it is not possible if #f(x)=0#. So the Range is all Real values except #0#

Nathan Axel · Answer

undefined Domain: $x \in \mathbb{R}, x \neq 1$
Range: $f(x) \in \mathbb{R}, f(x) \neq 0$

Eva Abramson · Answer

undefined To find the domain and range of the function f(x) = 1 / (x - 1), we need to consider the restrictions on the input (x) and the output (f(x)).

Domain:
The domain of the function f(x) is all real numbers except for the value(s) that make the denominator zero, since division by zero is undefined. In this case, the denominator x - 1 cannot be equal to zero, so x ≠ 1. Therefore, the domain of f(x) is all real numbers except x = 1.

Range:
To find the range, we need to analyze the behavior of the function. As x approaches positive infinity or negative infinity, f(x) approaches 0. This means that the range of f(x) includes all real numbers except 0. Therefore, the range of f(x) is all real numbers except 0.