First slide

Functions (XII)

Question

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

Moderate

A

One
B

Two
C

Zero
D

Infinitely many

Solution

We have a^{f (x)} + g (x) = 0, a > 0
Since minimum value of g (x) is 1/2
$\begin{array}{ll} ∴ g (x) > 0 and a^{f (x)} > 0 \\ ∴ a^{f (x)} + g (x) > 0, \forall x \end{array}$
Hence number of solutions is zero.

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