Question

What are the domain and the range of$y=secx$?

Short answer

The domain of $y=secx$is $\{\overline{)x}x\ne$odd integer multiples of $\frac{\mathrm{\pi }}{2}\}$and range is$y\le -1$and$y\ge 1$.

Step-by-step solution

Step 1. Given information.

We have given function$y=secx$.

Step 2. Domain of the function.

For secant function,$\theta$lies between the interval $(0,\pi )$.But for odd multiples of$\frac{\mathrm{\pi }}{2}$the value of secant function will be undefined.

So, domain of the$sec\theta$is$(\overline{)x}x\ne$odd integer multiples of $\frac{\mathrm{\pi }}{2}$}.

Step 3. Range of the function.

$Sec\theta =\frac{1}{y}$, Range of the function will be$-1\le \frac{1}{y}\le 1$.

So,$y\le -1$and$y\ge 1$.