Given that #f(x) = sqrtx - 3# and g(x) = 2x + 1, how do you find #(f/g)(-sqrt3)#?

Answer 1

To find ((f/g)(-\sqrt{3})), substitute (-\sqrt{3}) into both (f(x)) and (g(x)), then divide the resulting values of (f(x)) and (g(x)).

First, (f(-\sqrt{3}) = \sqrt{-\sqrt{3}} - 3).

Second, (g(-\sqrt{3}) = 2(-\sqrt{3}) + 1).

Third, divide the result of (f(-\sqrt{3})) by the result of (g(-\sqrt{3})) to get ((f/g)(-\sqrt{3})).

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Answer 2

Ethan Adkins

See a solution process below:

First, we can write #(f/g)(x)# as:

#(f/g)(x) = (sqrt(x) - 3)/(2x + 1)#

To find #(f/g)(-sqrt(3))# we need to substitute #color(red)(-3)# for each occurrence of #color(red)(x)# in #(f/g)(x)#:

#(f/g)(color(red)(x)) = (sqrt(color(red)(x)) - 3)/(2color(red)(x) + 1)# becomes:

#(f/g)(color(red)(-sqrt(3))) = (sqrt(color(red)(-sqrt(3))) - 3)/((2 * color(red)(-sqrt(3))) + 1)#

#(f/g)(color(red)(-sqrt(3))) = (sqrt(color(red)(-sqrt(3))) - 3)/((-2color(red)(sqrt(3)) + 1)#

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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.