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Gega · Answer 1 · 2023-12-15T20:14:56+0000

Solution:

Given:

The domain is the set of all possible x-values (inputs) that will make the function (output) to be real and defined.

To get the domain of the function given, we need to get the undefined or singularity points.

$\begin{gathered} f(x)\text{ will be defined only when the denominator is equal to 0.} \\ \text{Hence, singularity or undefined points will occur when,} \\ x^2-6x+8=0 \\ \text{Solving to get these points,} \\ x^2-4x-2x+8=0 \\ x(x-4)-2(x-4)=0 \\ (x-2)(x-4)=0 \\ x-2=0 \\ x=0+2 \\ x=2 \\ \\ OR \\ x-4=0 \\ x=0+4 \\ x=4 \\ \\ \text{Hence, singularity occurs at;} \\ x=2,x=4 \end{gathered}$

The domain of the function will exist when;

$\begin{gathered} x\\e2,x\\e4 \\ \\ \text{Hence, the solution to the domain of the function is;} \\ x<2\text{ OR }24 \end{gathered}$

Hence, the solution to the domain is;

$x<2\text{ OR }24$

In interval notation, the domain is;

$(-\infty,2)\cup(2,4)\cup(4,\infty)$

Therefore, the final answer is;

All real numbers except 2 and 4.

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