SOLUTION: Evaluate the function. Given that f(x) = (sqrt x^2+1)/(x-1) , find f(-3). A) (sqrt 10)/(-4) ≈ -0.7906 B) (sqrt 10)/(-4) ≈ 0.7906 C) (sqrt 10)/(-4) ≈ -25.

Question 201560: Evaluate the function.
Given that f(x) = (sqrt x^2+1)/(x-1) , find f(-3).
A) (sqrt 10)/(-4) ≈ -0.7906
B) (sqrt 10)/(-4) ≈ 0.7906
C) (sqrt 10)/(-4) ≈ -25.0000
D) (sqrt 10)/(-4) ≈ -1.25
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Just substitute -3 in place of

and do the arithmetic. But since you are given 4 answers, let's look at them. They are all

. Since

is positive (by convention -- the negative square root would be designated

), and the denominator is clearly negative, the quotient must be negative. Goodbye Answer B.

If it were Answer C, then

would have to be equal to 100. Since we know that

is less than 10, that can't be true. Goodbye, Answer C.

If it is Answer D, then

has to be larger than 4, but if it is Answer A, then

has to be smaller than 4. We know that 3 times 3 equals 9, so 3 is smaller than the square root of 10, but 4 times 4 is 16, so 4 is larger than the square root of 10.

And I never touched a calculator...

John

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SOLUTION: Evaluate the function. Given that f(x) = (sqrt x^2+1)/(x-1) , find f(-3). A) (sqrt 10)/(-4) &#8776; -0.7906 B) (sqrt 10)/(-4) &#8776; 0.7906 C) (sqrt 10)/(-4) &#8776; -25.

SOLUTION: Evaluate the function. Given that f(x) = (sqrt x^2+1)/(x-1) , find f(-3). A) (sqrt 10)/(-4) ≈ -0.7906 B) (sqrt 10)/(-4) ≈ 0.7906 C) (sqrt 10)/(-4) ≈ -25.