The number of solutions of the equation f f x - g x -0- a -0- g x -0 and has minimum value of 1-2 isA- oneB- zeroC- infinitely manyD- two

The correct option is B zeroHere, a gt; 0 ⇒ a^f(x) gt; 0, as exponential is always positive. And given, g(x) gt; 1/2⇒ a^f(x) g (x) gt; 0 for all x. ...

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Standard XII

Mathematics

Inequalities Involving Modulus Function

The number of...

Question

The number of solutions of the equation $a^{f (x)}$ + g(x) = 0, a > 0, g (x) $\neq$ 0 and has minimum value of $\frac{1}{2}$ is

one

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two

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zero

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infinitely many

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Solution

The correct option is C zero
Here, a > 0 $\Rightarrow$ $a^{f (x)}$ > 0, as exponential is always positive.
And given, g(x) > $\frac{1}{2} \Rightarrow a^{f (x)}$ g (x) > 0 for all x.
Hence, no solution.

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The number of solutions of the equation af(x) + g(x) = 0, a > 0, g (x) ≠ 0 and has minimum value of 12 is

The correct option is C zeroHere, a > 0 ⇒ af(x) > 0, as exponential is always positive. And given, g(x) > 12⇒af(x) g (x) > 0 for all x. Hence, no solution.

The number of solutions of the equation $a^{f (x)}$ + g(x) = 0, a > 0, g (x) $\neq$ 0 and has minimum value of $\frac{1}{2}$ is

The correct option is C zero
Here, a > 0 $\Rightarrow$ $a^{f (x)}$ > 0, as exponential is always positive.
And given, g(x) > $\frac{1}{2} \Rightarrow a^{f (x)}$ g (x) > 0 for all x.
Hence, no solution.