Question

How do you find the domain & range for `f(T)=sec(piT/4)`?

Answer 1

Since `sec(x)=1/cos(x)`, and since you can't divide by zero, the domain is composed by all the points such that `cos((Tpi)/4)\ne 0`.

This means that:

• `(Tpi)/4 \ne \pi/2 + 2k\pi`

• `(Tpi)/4 \ne (3\pi)/2 + 2k\pi`

Solving for `T`:

• `T \ne 2 + 4k`

• `T \ne 6 + 4k`.

As for the range, since the function has vertical asymptote, and the denominator changes sign as it crosses zero, we have that

`lim_{T\to 6^{\pm}} 1/cos((T\pi)/4) = 1/0^{\pm}=\pm \infty`