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How do you find domain and range for # f(x) = sqrt(7x + 2)#?

Answer 1

Savannah Anderson

The domain is #x in [-2/7, +oo)#. The range is #y in [0,+oo)#

Let #y=sqrt(7x+2)#

What's under the square root sign is #>=0#

Consequently,

#7x+2>=0#

#=>#, #x>=-2/7#

The domain is #x in [-2/7, +oo)#

When

#x=-2/7#, #=>#, #y=0#

Additionally

#lim_(x->+oo)sqrt(7x+2)=+oo#

Consequently,

The range is #y in [0,+oo)#

plot{sqrt(7x+2) [-7.06, 21.42, -7.46, 6.78]}

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Answer 2

Nathan Axel

Domain: (7x + 2 \geq 0) since the square root of a negative number is undefined in the real number system. [ \text{Domain: } x \geq -\frac{2}{7} ]

Range: The square root of any real number is non-negative. [ \text{Range: } f(x) \geq 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.