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Question

Let f(x)=42x and g(x)=(xa)(xa+3). If g(f(x))<0  xDf, then the complete set of values of a is
[Df denotes the domain of the function f]
  1. (2,5)
  2. (2,3)
  3. (0,3)
  4. (0,5)


Solution

The correct option is B (2,3)
f(x)=42x 
42x0
162x
x14
and 2x0x2
Df=[14,2]
Range of f is [0,2]

g(x)=(xa)(xa+3)
g(f(x))<0  f(x)[0,2]
g(0)<0 and g(2)<0
a(a+3)<0 and (2a)(5a)<0
a(0,3)    (1) and a(2,5)    (2)

From (1) and (2), we get
a(2,3)

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