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Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box. ƒ -1(x) = a0 x a1 a2 ƒ -1(4) = a3

Respuesta :

choixongdong
ƒ(x) = 1/2x + 4

inverse

x = 1/2 y + 4
2x = y + 8
y = 2x - 8
so inverse f-1(x) = 2x - 8

ƒ -1(4) = 2(4)  - 8 = 0

answer

ƒ -1(x) = 2x - 8
ƒ -1(4) = 0
manuelatuozzo

Answer:

[tex]f^{-1}(x) = 2x - 8\\ f^{-1}(4) = 0[/tex]

Step-by-step explanation:

To find an inverse function, we need to think the function as an equality x = 1/2y + 4 that we have to resolve for the y.

First, let's subtract 4 from both sides.

x - 4 = 1/2y + 4 - 4

x - 4 = 1/2y

Now we multiply by 2 on both sides.

(x-4)*2 = 1/2y*2

2*x-8 = y

Therefore, the inverse function is

[tex]f^{-1}(x)=2x-8[/tex]

To find out [tex]f^{-1}(4)[/tex], we need to replace the x of the function with a 4:

[tex]f^{-1}(4)[/tex] = 2*4 - 8 = 8 - 8 = 0

[tex]f^{-1}(4)[/tex]= 0