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Differential Calculus

Blazing goIITian

Joined:	11 Jan 2009
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16 May 2009 14:13:53 IST

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The domain of the real valued function f(x) for which 4^f(x) + 4^{1 - f(x)} = 4^x is

(a) (-1, 1]

(b) [1, +infinity)

(d) (-infinity, -1]

Source: Problems Plus in IIT Mathematics by A Das Gupta

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Comments (3)

eragon24

Blazing goIITian

Joined: 14 May 2009

Posts: 697

16 May 2009 14:44:04 IST

Like 3 people liked this

ans b.[1,infinity)

liquid ice

Cool goIITian

Joined: 16 May 2009

Posts: 96

16 May 2009 14:50:06 IST

Like 2 people liked this

make quadratic eqn i.e. 4^2y + 4 - 4^x 4^y = 0

using quadratic formula 4^2x - 16 >=0

hence b option is correct

Akshay

Blazing goIITian

Joined: 27 Dec 2007

Posts: 689

16 May 2009 15:23:26 IST

Like 1 people liked this

y=f(x)
so 4^y+4/4^y=4^x

therefore t²-4^xt+4=0 t=4^y

t>0 for all x and

solve for t=4^x+-sqrt(4^2x-16)/2

now f is defined if t is real and positive

therefore, 4^2x-16>=0

4^2x>=16

2x>=2

x>=1

further, we can see that if t is real, it i always positive.

hence f is defined if x>=1

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