Chapter 7: Q 1. (page 457)

What are the domain and the range of $y = s e c x$ ?

Short Answer

Expert verified

The domain of $y = s e c x$ is ${x x \neq$ odd integer multiples of $\frac{π}{2}}$ and range is $y \leq - 1$ and $y \geq 1$ .

Step by step solution

Step 1. Given information.

We have given function $y = s e c x$ .

Step 2. Domain of the function.

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

So, domain of the $s e c θ$ is $(x x \neq$ odd integer multiples of $\frac{π}{2}$ }.

Step 3. Range of the function.

$S e c θ = \frac{1}{y}$ , Range of the function will be $- 1 \leq \frac{1}{y} \leq 1$ .

So, $y \leq - 1$ and $y \geq 1$ .

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What are the domain and the range of $y = s e c x$ ?

Short Answer

Step by step solution

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Step 2. Domain of the function.

Step 3. Range of the function.

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