Question

the sets of all values of 'x' satisfying 16power 1/x ÷ 2power x+3
​

Answer 1

Step-by-step explanation:

1−f(x)−f(x)

2

>f(1−5x)

Or

f(f(x))>f(1−5x) ...(i)

Now

f

′

(x)=−1−3x

2

Hence

f

′

(x)<0 for all x. ...(ii)

Hence

f(f(x)>f(1−5x)

But f(x) is a decreasing function (from ii).

Hence

f(x)<1−5x

Or

1−x−x

3

<1−5x.

Or

4x−x

3

<0

Or

x

3

−4x>0

Or

x(x

2

−4)>0

Or

x>0 and x

2

−4>0 or

x<0 and x

2

−4<0

Hence if x>0 x

2

−4>0 implies xϵ(2,∞)

And

x<0 and x

2

−4<0 implies (−2,0)

Hence

xϵ(−2,0)∪(2,∞).