To determine whether the function [tex]\( F(x) = \frac{6}{x-6} \)[/tex] can ever be equal to zero, let's analyze the function step by step.
The function [tex]\( F(x) = \frac{6}{x-6} \)[/tex] is a rational function where the numerator is 6 and the denominator is [tex]\( x-6 \)[/tex].
For a rational function [tex]\( \frac{a}{b(x)} \)[/tex] to be equal to zero, the numerator [tex]\( a \)[/tex] must be zero. However, in this function:
- The numerator is a constant 6, which is never zero.
Therefore, no matter what value [tex]\( x \)[/tex] takes (as long as [tex]\( x \neq 6 \)[/tex]), the fraction [tex]\( \frac{6}{x-6} \)[/tex] cannot be zero because the numerator is never zero.
### Conclusion:
The function [tex]\( F(x) = \frac{6}{x-6} \)[/tex] is never equal to zero. Thus, the statement is:
A. True
