Question

Determine a lei da função inversa de cada função dada:
y = x – 8

y = 2x - 4

f(x) = 2x + 5

f(x) = 4x + 2

y = 3x – 5

Answer 1

Resposta:

Explicação passo-a-passo:

1)

y = x-8

x = y - 8

y = x + 8

2)

y = 2x -4

x = 2y - 4

2y = x+4

y = x/2 +2

3)

y = 2x +5

x = 2y +5

2y = x -5

y = x-5 / 2

4)

y = 4x +2

x = 4y +2

4y = x-2

y = x -2 /4

5)

y = 3x - 5

x = 3y - 5

3y = x+5

y = x+5 / 3

Answer 2

Explicação passo-a-passo:

a) $\sf y=x-8$

Substituindo $\sf x~por~y~e~y~por~x$:

$\sf x=y-8$

Isolando $\sf y$:

$\sf y=x+8$

$\sf \red{f^{-1}(x)=x+8}$

b) $\sf y=2x-4$

Substituindo $\sf x~por~y~e~y~por~x$:

$\sf x=2y-4$

Isolando $\sf y$:

$\sf 2y=x+4$

$\sf y=\dfrac{x+4}{2}$

$\sf \red{f^{-1}(x)=\dfrac{x+4}{2}}$

c) $\sf f(x)=2x+5$

$\sf y=2x+5$

Substituindo $\sf x~por~y~e~y~por~x$:

$\sf x=2y+5$

Isolando $\sf y$:

$\sf 2y=x-5$

$\sf y=\dfrac{x-5}{2}$

$\sf \red{f^{-1}(x)=\dfrac{x-5}{2}}$

d) $\sf f(x)=4x+2$

$\sf y=4x+2$

Substituindo $\sf x~por~y~e~y~por~x$:

$\sf x=4y+2$

Isolando $\sf y$:

$\sf 4y=x-2$

$\sf y=\dfrac{x-2}{4}$

$\sf \red{f^{-1}(x)=\dfrac{x-2}{4}}$

e) $\sf y=3x-5$

Substituindo $\sf x~por~y~e~y~por~x$:

$\sf x=3y-5$

Isolando $\sf y$:

$\sf 3y=x+5$

$\sf y=\dfrac{x+5}{3}$

$\sf \red{f^{-1}(x)=\dfrac{x+5}{3}}$