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dusya [7]
3 years ago
16

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

Mathematics
2 answers:
Sergeu [11.5K]3 years ago
8 0

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=\dfrac{x-1}{2}

astra-53 [7]3 years ago
8 0

Answer:

h(x) =  \frac{1x}{2} -\frac{1}{2}

Step-by-step 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 = \frac{x-1}{2}.

We can write

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

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

h(x) =  \frac{1x}{2} -\frac{1}{2}

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

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