Answer:
C
Step-by-step explanation:
We are given that a function
[tex]f(x)=(\frac{1}{2})^x[/tex]
It can be write as
[tex]y=f(x)=2^{-x}[/tex]
Taking log on both sides
[tex]logy=-xlog2[/tex]
Differentiate w.r.t x
[tex]\frac{1}{y}\frac{dy}{dx}=-log 2[/tex]
[tex]\frac{d(logx)}{dx}=\frac{1}{x}[/tex]
[tex]\frac{dy}{dx}=-ylog2=-2^{-x}log2<0[/tex] for all x
When f'(x) <0 then function is decreasing.
Hence, given function is decreasing function.
Substitute x=0 then we get
[tex]f(0)=1[/tex] Because ([tex]a^0=1[/tex])
Therefore, y intercept is (0,1).
Domain pf function f(x)=R
Range of given function :([tex]0,\infty[/tex])
Hence, option C is true.
