Question

Evaluate the exponential function ƒ(x) = (1/2)^x

Answer 1

Answer:

D. 2 is correct.

Step-by-step explanation:

We are given the function, $f(x)=(\frac{1}{2})^{x}$

It is required to find the value of f(x) when x = -1.

So, we will substitute the value of x= -1 in the function.

This gives us,

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

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

As, we know,

$(\frac{1}{b})^{-1}=\frac{1}{b^{-1}}=b$

So, $f(-1)=(\frac{1}{2})^{-1}$ implies $f(-1)=2$.

Hence, the value that completes the table is 2.

So, option D is correct.

Answer 2

For this case we have the following exponential function:
 $f(x) = (\frac{1}{2})^x$
 Evaluating the function for x = -1 we have:
 $f(x)=(\frac{1}{2})^{-1}$
 By power properties we can rewrite the function.
 We have then:
 $f(x)= \frac{1}{(\frac{1}{2})^1}$
 $f(x)= \frac{1}{\frac{1}{2}}$
 $f(x) = 2$
 Answer:
 The value that completes the table when x = -1 is:
 $f(x) = 2$
 D. 2