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What is the domain of #f(x)=arcsin(5x-4)#?

Answer 1

Brooklyn Anderson

Domain; #x in [ 0.6, 1 ]#.

The range is # y in [ -pi/2, pi/2 ]#.

Here, #X = 5x- 4 in [ - 1, 1 ]#

#rArr x in [ 0.6, 1 ]# See graph. graph{(y-arcsin(5x-4))=0[0.6 1 -1 1]}

The inverse is #x = 0.2 sin y + 0.8, the graph of the inverse is

unrestricted. See the y-unlimited inverse wavy graph, with period #2pi# and

amplitude 0.2,

graph{x - 0.2 sin y - 0.8=0[0 2 -10 10]}

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Answer 2

Oliver Atkinson

The domain of ( f(x) = \arcsin(5x - 4) ) is the set of all real numbers such that ( 5x - 4 ) is within the range of the arcsin function, which is ([-1, 1]). So, the domain is (\left[\frac{3}{5}, \frac{5}{5}\right]), or equivalently, (\left[\frac{3}{5}, 1\right]).

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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.