Question

Calcule o valor de cada função abaixo nos pontos - 2, - 1, 2 e 3.

A)
$f(x) = 7 {}^{x}$

B)
$g(x) = 18 \times ( \frac{1}{3} ) {}^{x}$

C)
$h(x) = \frac{4}{3} {}^{x}$

D)
$i(x) = ( \frac{1}{4} ) {}^{x} + 2$

E)
$j(x) = ( \frac{2}{5} ) {}^{x} + \frac{3}{5}$

F)
$k(x) = (27 \frac{1}{3}) {}^{x}$
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Answer 1

A)
f(-2) = 7^-2
f(-2) = 1/7^2
f(-2) = 1/49

f(-1) = 7^-1
f(-1) = 1/7

f(2) = 7^2
f(2) = 49

f(3) = 7^3
f(3) = 343

B)
g(-2) = 18 x (1/3)^-2
g(-2) = 18 x 3^2
g(-2) = 18 x 9
g(-2) = 162

g(-1) = 18 x (1/3)^-1
g(-1) = 18 x 3
g(-1) = 54

g(2) = 18 x (1/3)^2
g(2) = 18 x 1/9
g(2) = 18/9
g(2) = 2

g(3) = 18 x (1/3)^3
g(3) = 18 x 1/27
g(3) = 18/27
g(3) = 2/3

C)
h(-2) = (4/3)^-2
h(-2) = (3/4)^2
h(-2) = 9/16

h(-1) = (4/3)^-1
h(-1) = 3/4

h(2) = (4/3)^2
h(2) = 16/3
h(2) = 8

h(3) = (4/3)^3
h(3) = 48/27
h(3) = 16/9

D)
i(-2) = (1/4)^-2 + 2
i(-2) = 4^2 + 2
i(-2) = 16 + 2
i(-2) = 18

i(-1) = (1/4)^-1 + 2
i(-1) = 4 + 2
i(-1) = 6

i(2) = (1/4)^2 + 2
i(2) = 1/16 + 2
i(2) = 1/16 + 32/16
i(2) = 33/16

i(3) = (1/4)^3 + 2
i(3) = (1/4)^3 + 2
i(3) = 1/64 + 2
i(3) = 1/64 + 128/64
i(3) = 129/64

E)
j(-2) = (2/5)^-2 + 3/5
j(-2) = (5/2)^2 + 3/5
j(-2) = 25/4 + 3/5
j(-2) = 125/20 + 12/20
j(-2) = 137/20

j(-1) = (2/5)^-1 + 3/5
j(-1) = 5/2 + 3/5
j(-1) = 25/10 + 6/10
j(-1) = 31/10

j(2) = (2/5)^2 + 3/5
j(2) = 4/25 + 3/5
j(2) = 4/25 + 15/25
j(2) = 20/25
j(2) = 4/5

j(3) = (2/5)^3 + 3/5
j(3) = 8/125 + 3/5
j(3) = 8/125 + 75/125
j(3) = 83/125

k(-2) = (27 x 1/3) ^-2
k(-2) = 27^-2 x (1/3)^-2
k(-2) = 1/27^2 x 3/1^2
k(-2) = 1/729 x 9/1
k(-2) = 9/729
k(-2) = 1/81

k(-1) = (27)^-1 x (1/3)^-1
k(-1) = 1/27 x 3/1
k(-1) = 3/27
k(-1) = 1/9

k(2) = (27)^2 x (1/3)^2
k(2) = 729 x 1/9
k(2) = 729/9
k(2) = 81

k(3) = (27)^3 x (1/3)^3
k(3) = 19.683 x 1/27
k(3) = 19683/27
k(3) = 729

Answer 2

Explicação passo-a-passo:

A)

f(-2) = 7^-2

f(-2) = 1/7^2

f(-2) = 1/49

f(-1) = 7^-1

f(-1) = 1/7

f(2) = 7^2

f(2)=49

f(3) = 7^3

f(3) = 343

B)

g(-2) = 18 x (1/3)^-2

g(-2) = 18 x 3^2

g(-2) = 18 x 9

g(-2) = 162

g(-1) = 18 x (1/3)^-1

g(-1) = 18 x 3

g(-1) = 54

g(2) = 18 x (1/3)^2

g(2) = 18 x 1/9

g(2) = 18/9

g(2) = 2

g(3) = 18 x (1/3)^3

g(3) = 18 x 1/27

g(3) = 18/27

g(3) = 2/3

C)

h(-2) = (4/3)^-2

h(-2) = (3/4)^2

h(-2) = 9/16

h(-1) = (4/3)^-1

h(-1) = 3/4

h(2) = (4/3)^2

h(2) = 16/3

h(2) = 8

h(3) = (4/3)^3

h(3) = 48/27

h(3)=16/9

D)

i(-2) = (1/4)^-2 + 2

i(-2) = 4^2 + 2

i(-2) = 16 + 2

i(-2) = 18

i(-1) = (1/4)^-1 + 2

i(-1) = 4 + 2

i(-1) = 6

i(2) = (1/4)^2 + 2

i(2) = 1/16 + 2

i(2) = 1/16 + 32/16

i(2) = 33/16

i(3) = (1/4)^3 + 2

i(3) = (1/4)^3 + 2

i(3) = 1/64 + 2

i(3) = 1/64 + 128/64

i(3) = 129/64

E)

j(-2) = (2/5)^-2 + 3/5

j(-2) = (5/2)^2 + 3/5

j(-2) = 25/4 + 3/5

j(-2) = 125/20 + 12/20

j(-2) = 137/20

j(-1) = (2/5)^-1 + 3/5

j(-1) = 5/2 + 3/5

j(-1) = 25/10 + 6/10

j(-1) = 31/10

j(2) = (2/5)^2 + 3/5

j(2) = 4/25 + 3/5

j(2) = 4/25 + 15/25

j(2) = 20/25

j(2) = 4/5

j(3) = (2/5)^3 + 3/5

j(3) = 8/125 + 3/5

j(3) = 8/125 + 75/125

j(3) = 83/125

F)

k(-2) = (27 x 1/3) ^-2

k(-2) = 27^-2 x (1/3)^-2

k(-2) = 1/27^2 x 3/1^2

k(-2) = 1/729 x 9/1

k(-2) = 9/729

k(-2) = 1/81

k(-1) = (27)^-1 x (1/3)^-1

k(-1) = 1/27 x 3/1

k(-1) = 3/27

k(-1)=1/9

k(2) = (27)^2 x (1/3)^2

k(2) = 729 x 1/9

k(2) = 729/9

k(2) = 81

k(3) = (27)^3 x (1/3)^3

k(3) = 19.683 x 1/27

k(3) = 19683/27

k(3) = 729