For the every value of x the function f(x) = 1 5^x is - Vidyadip

MCQ

For the every value of $ x$ the function $f(x) = {1 \over {{5^x}}}$ is

✓
Decreasing
B
Increasing
C
Neither increasing nor decreasing
D
Increasing for $x > 0 $ and decreasing for $x < 0$

✓

Answer

Correct option: A.

Decreasing

a
(a) $f(x) = {5^{ - x}}$

==>$f'(x) = - {5^{ - x}}{\log _e}5 = - \frac{{{{\log }_e}5}}{{{5^x}}}$

==> $f'(x) < 0$ for all $x$

$i.e.,$ $f(x)$ is decreasing for all $x.$

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