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What is the domain of the function: #f(x) =sqrt(( x- (3x^2)))#?

Answer 1

Eva Abramson

#D_f=[0,1/3]#

#x-3x^2>=0# #3x^2-x<=0# Lets solve the eq #3x^2-x=0# #x(3x-1)=0# #x=0 vv x=1/3#

Graph of #3x^2-x#:

graph{3x^2-x [-1.351, 1.35, -0.676, 0.675]}

So, #3x^2-x<=0# below the #x#-axis, or in the other words between zeros we have found: #3x^2-x<=0 <=> x in [0,1/3]#

#D_f=[0,1/3]#

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Answer 2

Eli Assouline

The domain of the function f(x) = sqrt(x - 3x^2) is all real numbers such that x - 3x^2 ≥ 0. This inequality simplifies to x(1 - 3x) ≥ 0. Solving this inequality gives the domain as (-∞, 1/3] ∪ [0, ∞).

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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.