Question

Which of these statements is true for f(x)=(1/2)^x ?

A. It is always increasing.
B. The domain of f(x) is x > 0.
C. The y-intercept is (0, 1).
D. The range of f(x) is y>1/2 .

Answer 1

The answer is c

Explanation:

Answer 2

C

Explanation:

We are given that a function

`f(x)=((1)/(2))^x`

It can be write as

`y=f(x)=2^(-x)`

Taking log on both sides

`logy=-xlog2`

Differentiate w.r.t x

`(1)/(y)(dy)/(dx)=-log 2`

`(d(logx))/(dx)=(1)/(x)`

`(dy)/(dx)=-ylog2=-2^(-x)log2<0` for all x

When f'(x) <0 then function is decreasing.

Hence, given function is decreasing function.

Substitute x=0 then we get

`f(0)=1` Because (
`a^0=1`)

Therefore, y intercept is (0,1).

Domain pf function f(x)=R

Range of given function :(
`0,\infty`)

Hence, option C is true.