Respuesta :

saya
Inverses are easy for this problem. First we start with the equation. Then we change the f(x) to y to make this whole problem easier. 
y=2x+1
Isolate the x and solve for x. 
x=(y-1/2)
Switch x and y again. 
y=(x-1/2)
Add function notation.
f^-1(x)=(x-1/2)
Done! And if you need to check if equations are inverses, add the original equation into the x variable of the inverse. The solution should be f^-1(x)=x. That means the inverse is right.


pemanuel

Answer:

[tex]f^{-1}(x)=\frac{x}{2}+\frac{1}{2}.[/tex]

Step-by-step explanation:

As we have a lineal function, there is a easy way to find the inverse [tex]f^{-1}(x)[/tex]:

First, switch the x and y, that is if we have

y = f(x) = 2x-1, then after the change we obtain

x = 2y-1.

Then, clear y:

[tex]x = 2y-1[/tex]

[tex]x+1 = 2y[/tex]

[tex]\frac{x+1}{2} = y[/tex]

[tex]\frac{x}{2}+\frac{1}{2} = y.[/tex]

Then, [tex]f^{-1}(x)=\frac{x}{2}+\frac{1}{2}[/tex] is the inverse of y=2x-1.

You can check it composing both functions, if you obtain x the inverse is correct.

[tex]f(f^{-1}(x))= 2(\frac{x}{2}+\frac{1}{2})-1[/tex]

[tex]f(f^{-1}(x)) = \frac{2x}{2}+\frac{2}{2}-1[/tex]

[tex]f(f^{-1}(x)) = x+1-1[/tex]

[tex]f(f^{-1}(x)) = x.[/tex]

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