Answered

"Domain of Functions: Consider the function
f(x)=(\sqrt(x-2))/(x-4) Discuss the constraints on x
imposed by the numerator and denominator. Derive the domain of
the function and explain your reasoning"



Answer :

jacob193

Answer:

[tex]x \ge 2[/tex] and [tex]x \ne 4[/tex].

Step-by-step explanation:

In the given function [tex]f(x) = (\sqrt{x - 2}) / (x - 4)[/tex], there are two constraints:

  • Input to the square root function must be non-negative (greater than or equal to [tex]0[/tex]): [tex](x - 2) \ge 0[/tex].
  • The denominator must be non-zero: [tex]x - 4 \ne 0[/tex].

For a value of [tex]x[/tex] to be in the domain of this function, both requirements must be satisfied. Simplify both inequalities to obtain their intersection:

[tex]x \ge 2[/tex] and [tex]x \ne 4[/tex].