Considering the domain of the function, it is restricted for:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
What is the domain of a function?
The domain of a function is the set that contains all possible input values for the function.
A fraction cannot have a denominator of zero, hence:
- [tex]4x^2 - 12x \neq 0[/tex].
- [tex]-x^2 + 5x - 6 \neq 0[/tex].
We solve these two inequalities to find the restrictions, hence:
[tex]4x^2 - 12x \neq 0[/tex]
[tex]4x(x - 3) \neq 0[/tex]
[tex]4x \neq 0 \rightarrow x \neq 0[/tex]
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
[tex]-x^2 + 5x - 6 \neq 0[/tex].
[tex]x^2 - 5x + 6 \neq 0[/tex]
[tex](x - 3)(x - 2) \neq 0[/tex]
[tex]x - 2 \neq 0 \rightarrow x \neq 2[/tex].
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
Hence the correct option is:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
More can be learned about the domain of a function at https://brainly.com/question/10891721
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