Question

For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.

Options

• neither increasing nor decreasing

• decreasing

• constant

• increasing

Answer 1

For every value of x, the function f(x) = `1/"a"^x`, a > 0 is decreasing.

Explanation:

We have,

f(x) = `1/"a"^x = "a"^-x`, a > 0

f'(x) = - a^-x log a

f'(x) = `(- log "a")/"a"^x`

f'(x) < 0 ∀ x ∈ R, a >0

∴ f(x) is decreasing for every value of x.