The function 𝑚 is given by           𝑚⁡(𝑥)=3⁢tan⁡(𝑥+𝜋2).Find all values in the domain of 𝑚 that yield an output value of 1.

To find the values in the domain of m that yield an output value of 1, we need to solve the equation m(x) = 1 for x.

Given m(x) = 3tan(x + π/2), we first set m(x) = 1:

1 = 3tan(x + π/2)

We then divide both sides by 3 to isolate the tan function:

1/3 = tan(x + π/2)

Next, we apply the inverse tangent function (also known as the arctangent or atan function) to both sides to solve for x + π/2:

atan(1/3) = x + π/2

Subtract π/2 from both sides to solve for x:

x = atan(1/3) - π/2

The atan function has a period of π, so the general solution for x is:

x = atan(1/3) - π/2 + kπ

where k is an integer.

This gives us all the values in the domain of m that yield an output value of 1.