Respuesta :

calculista

we have

[tex] f(x) = \frac{1}{2}x + 10 [/tex]

Step [tex] 1 [/tex]

Let

y=f(x)

[tex] y = \frac{1}{2}x + 10 [/tex]

Exchange the variable x for y and variable y for x

[tex] x = \frac{1}{2}y + 10 [/tex]

Clear variable y

Multiply by [tex] 2 [/tex] both sides

[tex] 2x = y + 20 [/tex]

[tex] y = 2x-20 [/tex]

Let

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

[tex] f(x)^{-1}=2x-20 [/tex]

therefore

the answer is

the inverse of the function is [tex] f(x)^{-1}=2x-20 [/tex]

the missing value is [tex] 20 [/tex]

Answer:

The Given function is

y= x + 10

To find the inverse of function , we use the following procedure

x=y-10

Now, replace x by y and y by x, we get the inverse of function

y=x -10 , is the inverse of the function, y=x+10.

As, it is given that inverse of f(x) is h(x)

Also, h(x)= 2 x - k-------(1)

Inverse of f(x)=x+10 is ,y= x-10, that is 2 y=2 x- 20------(2)

Comparing 1 and 2, gives

h(x)=2 y

-k=-20

k=20

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