the formula is {x ∈ dom(g) | g(x) ∈ dom(f)}
#i need help finding the domain of log(sin(x))
naive zodiac
quaint pecanBOT
naive zodiac
what i got so far is that
f(x) = log(x) and g(x) = sin(x)
and i put it into the formula but im not sure what to do
since the dom(sin(x)) would be {x ∈ R} and dom(log(x)) would be {x ∈ R | x > 0}
but if i put into the formula
then i get {x ∈ R | sin(x) ∈ x > 0}
but im not sure what to do next
naive zodiac
ohh ok thanks
do you know if you can help me out with finding the range?
if you have the time
compact spindle
Sure.
naive zodiac
ill show you my working out
compact spindle
So we know that sin(x) oscillates between -1 and 1, but in order to abide our restriction its going to be restricted to 0 < sin(x) <= 1. Note this is our input. Now the smaller the input the larger the negative exponent. Ex. log_10_(10^-1), log_10_(10^-10) as our input gets smaller and smaller i.e infinitely small towards 0, the larger the negative exponent gets. Now our largest input is 1. log_10_(1) = 0. Therefore I'd say the range is y <= 0
naive zodiac
the formula to find the range(f(g(x)) is f(range(g) ∩ dom(f))
let f(x) = log(x) and let g(x) = sin(x)
so first i found the range(sin(x)) which was:
-1 ≤ x ≤ 1
then the domain of log(x) which was:
x > 0
then i substitute into the formula which got me:
log(x)(-1 ≤ x ≤ 1 ∩ x > 0)
and now i dont know what to do next
compact spindle
the formula to find the range(f(g(x)) is f(range(g) ∩ dom(f))
let f(x) = log(x)...
Don't know how to express it with your notation
naive zodiac
So we know that sin(x) oscillates between -1 and 1, but in order to abide our re...
oh thanks, im gonna give myself a moment to try to understand it
naive zodiac
Don't know how to express it with your notation
wdym by my notation?
compact spindle
The notation that you are using, I was not taught that notation.
naive zodiac
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