Answer:
The function is given below as
[tex]y=secx[/tex]
Step 1:
Concept:
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values that will make the function "work", and will output real y-values.
Simplify the function given and find the value of x for which it is undefined
[tex]\begin{gathered} y=secx \\ y=\frac{1}{cosx} \\ for\text{ the fraction to be undefined} \\ cosx=0 \\ x=\cos^{-1}0 \\ x=\frac{\pi}{2}+n\pi \end{gathered}[/tex]
Hence,
With the calculation above, we will have that
[tex]domain\text{ }x\ne\frac{\pi}{2}+n\pi[/tex]
Step 2:
Calculate the range of the function
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.
The graph of the secant function looks like this: The domain of the function y=sec(x)=1cos(x) is again all real numbers except the values where cos(x) is equal to 0 , that is, the values π2+πn for all integers n . The range of the function is y≤−1 or y≥1 .
Hence,
The range of y=sec x is
[tex]\Rightarrow y\ge1ory\leq-1[/tex]
Hence,
The final answer is given in the image below
