First tell us what is the domain of:Originally Posted by alyren
f(x) = ln(x)
“... mathematics is only the art of saying the same thing in different words” - B. Russell
would that be all real numbers,except 10?
what is the domain of:Originally Posted by alyren
f(x) = ln(x)
It would be x > 0 [meaning all the real numbers greater than 0]
So in your case {f(x) = ln [1/(x-10)]} the domain is (x - 10) > 0
“... mathematics is only the art of saying the same thing in different words” - B. Russell
what about the (1/x-10),
x can't equal to 10?
can you show me step to solve it?
Maybe function f is defined this way:Originally Posted by alyren
[tex]f(x) \;=\; ln \left ( \frac{1}{x - 10} \right )[/tex]
If so, then we show the denominator by typing grouping symbols.
f(x) = ln(1/[x - 10])
Then you can write:
f(x) = ln(1) - ln(x - 10)
This can be simplified because ln(1) is a constant.
Do you know? Subtracting 10 from x causes the graph to shift 10 units to the right.
If you're familiar with the graph and domain of ln(x), then the graph and domain of ln(x - 10) should be clear to you.
If you're not familiar with the graph and domain of ln(x), then perhaps you are not ready for this exercise.
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
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