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The no. of solutions of the equation a^(...

The no. of solutions of the equation `a^(f(x)) + g(x)=0` where a>0 , and g(x) has minimum value of 1/2 is :-

A

One

B

Two

C

Infinitely many

D

Zero

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Verified by Experts

The correct Answer is:
D
`a^(f(x))=-g(x)le-1//2`, since `g(x)ge1//2` for all `x`. But this is not possible as `a^(f(x))gt0` for all `x`. Thus the number of solution is zero.
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