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Inequalities, domain and Intersections of Lines

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#1 The largest possible domain of the function f(x) = sqrt{[x-1]/[x+2]} is the set
(A) all x except x=-2
(B) x < -2 or x greater or = 1
(C) none of the above.
#2 The solution of the inequality (x-3)(x^2-3x+2) > 0 is
(A) 1 < x < 2 and x > 3
(B) x > 3
(C) none of the above.
#3 In the triangle whose sides are 3 , 4 , and 5 , theta is the angle between the sides of lengths 3 and 5 . What is cos theta ?
(A) 0.75
(B) 0.6
(C) not enough information is given to be determined.
#4 The intersection of the lines y- 2 = 3(x-3) and y=-x+3 is the point
(A) (5/2,1/2)
(B) (-2,-3)
(C) The lines do not intersect.

I am attaching file as well for clear problems

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A step by step solution is provided to all the problems. Inequalities, domains, and intersections of lines are examined.

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1• The largest possible domain of the function is the set
(A) all except
(B) or
(C) none of the above.

For this x+ 2 > 0 => x > -2 and x - 1 =>x

Thus the domain will be x

Answer: None of the ...

Solution provided by:
Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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