Question

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

Answer 1

Answer:

C

Step-by-step explanation:

We are given that a function

$f(x)=(\frac{1}{2})^x$

It can be write as

$y=f(x)=2^{-x}$

Taking log on both sides

$logy=-xlog2$

Differentiate w.r.t x

$\frac{1}{y}\frac{dy}{dx}=-log 2$

$\frac{d(logx)}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=-ylog2=-2^{-x}log2$ 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.

Answer 2

Answer:

The answer is c

Step-by-step explanation: