In order to invert a function, switch y and x in the definition, and solve for y again:
[tex]y=2x+1 \mapsto x=2y+1[/tex]
Solving for y, we have
[tex]x=2y+1\iff x-1=2y \iff y=\dfrac{x-1}{2}[/tex]
Answer:
h(x) = [tex]\frac{1x}{2} -\frac{1}{2}[/tex]
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 = [tex]\frac{x-1}{2}[/tex].
We can write
y= [tex]\frac{1x}{2} -\frac{1}{2}[/tex]
Step 4 : take y = inverse of f(x) = h(x)
h(x) = [tex]\frac{1x}{2} -\frac{1}{2}[/tex]
Therefore, h(x) = [tex]\frac{1x}{2} -\frac{1}{2}[/tex]
