Verified Answer :

calculista

we have

\(f(x) = \frac{1}{2}x + 10\)

Step \(1\)

Let

y=f(x)

\(y = \frac{1}{2}x + 10\)


Exchange the variable x for y and variable y for x

\(x = \frac{1}{2}y + 10\)

Clear variable y

Multiply by \(2\) both sides

\(2x = y + 20\)

\(y = 2x-20\)

Let

\(f(x)^{-1} =y\)

\(f(x)^{-1}=2x-20\)

therefore

the answer is

the inverse of the function is \(f(x)^{-1}=2x-20\)

the missing value is \(20\)

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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