What is the range of f(x) = -2*0.5^x?

Question

asked Jun 7, 2020 193k views

2 Answers

Cmbarbu · Answer 1 · 2020-06-11T16:14:17+0000

Answer:

The range is

B.
$y\:<\:0$

Explanation:

The given function is

f(x)=-2(0.5)^x

Let
y=-2(0.5)^x

The range refers to y-values for which x is defined.

We solve for x to get;

-(y)/(2) =0.5^x

$\log(-(y)/(2)) =\log(0.5)^x$

$\log(-(y)/(2)) =x\log(0.5)$

$x=(\log(-(y)/(2)) )/(\log(0.5))$

x is defined for;

$-(y)/(2)\:>\:0$

Multiply by -2 and reverse the inequality sign.

$\implies y\:<\:0$