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

x      -4    -1    0     1      3
ƒ(x) 16    ?    1    1/2   1/8

Which value completes this table?
A.12
B.8
C.4
D.2

Respuesta :

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

Answer:

D. 2 is correct.

Step-by-step explanation:

We are given the function, [tex]f(x)=(\frac{1}{2})^{x}[/tex]

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,

[tex]f(x)=(\frac{1}{2})^{x}[/tex]

implies [tex]f(-1)=(\frac{1}{2})^{-1}[/tex]

As, we know,

[tex](\frac{1}{b})^{-1}=\frac{1}{b^{-1}}=b[/tex]

So, [tex]f(-1)=(\frac{1}{2})^{-1}[/tex] implies [tex]f(-1)=2[/tex].

Hence, the value that completes the table is 2.

So, option D is correct.

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