shaythetealord
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f(x) = 4^x and g(x) = 4^1/2x
Use the values given in the table and the functions to determine the missing values.

A =
1/16
1/8
1/4
1/2

B =
0
1/2
1
2

C =
1
2
4
8

fx 4x and gx 412x Use the values given in the table and the functions to determine the missing values A 116 18 14 12 B 0 12 1 2 C 1 2 4 8 class=

Respuesta :

DeanR

There are a few different ways to do this one. We can just note


[tex] g(x) = 4^{\frac 1 2 x} = (4^\frac 1 2)^x = 2^x [/tex]


so


[tex] A=g(-2) = 2^{-2} = \frac 1 4,\quad \quad B=g(0)=2^0 = 1, \quad\quad C=g(2)=2^2=4[/tex]


That's one way. We might also note


[tex] g(x) = 4^{\frac 1 2 x} = (4^x)^{\frac 1 2 } = \sqrt{4^x} = \sqrt{f(x)}[/tex]


so we can just take the square root of the corresponding value of f,


[tex]A=\sqrt{\frac 1 {16}} = \frac 1 4, \quad \quad B=\sqrt{1}=1, \quad\quad C=\sqrt{16} =4[/tex]


Finally nothing prevents us from substituting directly into the given g(x):


[tex]A = g(-2) = 4^{\frac 1 2(-2)} = 4^{-1} = \frac 1 4 [/tex]


[tex]B = g(0) = 4^{\frac 1 2 (0)} = 4^0 = 1 [/tex]


[tex] C = g(2) = 4^{\frac 1 2 (2)} = 4^1 = 4 [/tex]


That's three different ways and they all give the same answer, which they have to, otherwise math doesn't work.


Answer: A=1/4, B=1, C=4



MrRoyal

Functions can be represented on graphs and tables.

The values of A, B and C are: 1/4, 1 and 4

The functions are given as:

[tex]\mathbf{f(x) = 4^x}[/tex]

[tex]\mathbf{g(x) = 4^{\frac 12x}}[/tex]

The value of A

x = -2, when g(x) = A.

So, we have:

[tex]\mathbf{g(-2) = 4^{\frac 12 \times -2} = A}[/tex]

[tex]\mathbf{4^{-1} = A}[/tex]

Express as a fraction

[tex]\mathbf{\frac 14 = A}[/tex]

So, we have:

[tex]\mathbf{A = \frac 14 }[/tex]

The value of B

x = 0, when g(x) = B.

So, we have:

[tex]\mathbf{g(0) = 4^{\frac 12 \times 0} = B}[/tex]

[tex]\mathbf{4^{0} = B}[/tex]

[tex]\mathbf{1 = B}[/tex]

So, we have:

[tex]\mathbf{B = 1}[/tex]

The value of C

x = 2, when g(x) = C.

So, we have:

[tex]\mathbf{g(2) = 4^{\frac 12 \times 2} = C}[/tex]

[tex]\mathbf{ 4^1 = C}[/tex]

[tex]\mathbf{4 = C}[/tex]

So, we have:

[tex]\mathbf{C = 4}[/tex]

Hence, the values of A, B and C are: 1/4, 1 and 4

Read more about functions at:

https://brainly.com/question/14418346

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