Question

What is the inverse of the function f(x) = 2x + 1?

h(x) = 1/2 x – 1/2
h(x) = 1/2 x + 1/2
h(x) = 1/2 x – 2
h(x) = 1/2 x + 2
What is the exact answer?

Answer 1

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

Answer 2

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

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

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

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

`h(x)=(x-1)/(2)\\h(x)=(x)/(2)-(1)/(2)`

Have a great day