Respuesta :

Answer: No, the inverse of y is y=tan(x)-pi/2


Solution

y=tan^(-1) (x+pi/2)

Solving for x:

tan(y)=x+pi/2

Subtracting pi/2 both sides of the equation:

tan(y)-pi/2 = x+pi/2-pi/2

tan(y)-pi/2 = x

x=tan(y)-pi/2

Changing x by y and y by x:

y=tan(x)-pi/2

Cricetus

Answer:

No.

Step-by-step explanation:

Here we have our original function as

[tex]y=tan(x-\frac{\pi}{2})[/tex]

in order to find its inverse , we will replace each x in above equation by y and y with x . And then we solve the new equation for y. LEt us see how :

Given

[tex]y=tan(x-\frac{\pi}{2})[/tex]

replacing x with y and y with x

[tex]x=tan(y-\frac{\pi}{2})[/tex]

taking tan inverse of x

[tex]tan^{-1}x=y-\frac{\pi}{2}[/tex]

adding [tex]\pi}{2}[/tex] on both hand sides

[tex]tan^{-1}x +\frac{\pi}{2}=y[/tex]

Hence our inverse is

[tex]y=tan^{-1}x +\frac{\pi}{2}[/tex]

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