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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