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Verified Answer :

sgautam5

h(x) = (x-1 ) /2 ...........

Answer:

\(h(x)=\frac{x}{2}-\frac{1}{2}\)

Step-by-step explanation:

Hello

Step1

Let f(x)=y

f(x) = 2x + 1

(1)y= 2x + 1  

to find the inverse of f(x)

Replace every x with a y and replace every y with an x

y= 2x + 1

replacing  

x=2y+1

Step 2

Now solve the equation for y

x=2y+1

subtract 1 on both sides

x-1=2y+1-1

x-1=2y

divide boths dies by 2

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

\(\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}\)

let this last equation h(x)= inverse of f(x)

\(h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}\)

Have a great day

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