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How do you find the domain of #g(x)=10/(4-5x)#?

Answer 1

Kennedy Adams

The denominator has to be not-zero, so:

#4-5x!=0rArrx!=4/5# or #(-oo,4/5)uu(4/5,+oo)#.

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Answer 2

Nathan Axel

To find the domain of ( g(x) = \frac{10}{4 - 5x} ), we need to determine the values of ( x ) for which the function is defined.

The function is defined for all real numbers except those that make the denominator zero, since division by zero is undefined.

So, we solve ( 4 - 5x \neq 0 ):

[ 4 - 5x \neq 0 ] [ 5x \neq 4 ] [ x \neq \frac{4}{5} ]

Therefore, the domain of ( g(x) ) is all real numbers except ( x = \frac{4}{5} ), expressed as ( x \in \mathbb{R} ) where ( x \neq \frac{4}{5} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.