Aptitude

Aptitude Questions and Answers

1

Functions f and g are defined by:

f(x) = 1/x + 3x and g(x) = -1/x + 6x - 4

The domain  of (f+g)(x) is:

a

(-infinity , 4) U (0 , + infinity)

b

(-infinity , 0) U (0 , + infinity)

c

(-infinity , 0) U (0 , 9)

d

None of these

correct answer b

(f + g)(x) = f(x) + g(x) = (1/x + 3x) + (-1/x + 6x - 4)

(f + g)(x) = 9 x - 4 

Domain of f + g is given by the interval (-infinity , 0) U (0 , + infinity)

2

The range of the function f(x)= x2 - 4x + 9 is:

a

[5 , 9]

b

[-5 , +infinity)

c

[5 , + infinity)

d

None of these

correct answer c

h(x) = x 2 - 4 x + 9 = x 2 - 4 x + 4 - 4 + 9 = (x - 2) 2 + 5

(x - 2) 2 >= 0

(x - 2) 2 + 5 >= 5

Hence minimum value h(x) can have is 5 and maximum can go upto + infinity. So the range is [5 , + infinity)

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