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

What is the inverse of the function f(x)= 2x+1​-example-1
User Hroest
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2 Answers

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In order to invert a function, switch y and x in the definition, and solve for y again:


y=2x+1 \mapsto x=2y+1

Solving for y, we have


x=2y+1\iff x-1=2y \iff y=(x-1)/(2)

User Paul Bastian
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0 votes

Answer:

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

Explanation:

Given : f(x)= 2x+1​

To find : what is the inverse of the function .

Solution : We have given

f(x)= 2x+1​

To find the inverse of the function :

Step 1: take y = f(x)

y = 2x + 1

Step 2: interchange the x and y

x = 2y +1.

Step 3: Solve for y

On subtracting both sides by 1

x -1 = 2y.

On dividing both sides by 2

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

We can write

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

Step 4 : take y = inverse of f(x) = h(x)

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

Therefore, h(x) =
(1x)/(2) -(1)/(2)

User Daniel Ruoso
by
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