Consider the following function fx 5x2 1 State the domain

Consider the following function. f(x) = 5/x^2 + 1 State the domain of the function. (Enter your answer using interval notation.) Identify any intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = y-intercept (x, y) =

Solution

f(x) =5/(x²+1)

The given function is a rational function. Therefore denominator should not be equal to 0

x²+1=0

x=-i,i

Since imaginary values makes the denominator 0. It means there is no real values which will make the denominator 0.

Hence domain=(-infinity,infinity)

x intercept

To find the x intercept, we have to plug f(x)=0 and solve for x

0=5/(x²+1)

We cant solve this equation for x

so we dont have x intercept here

Hence, x intercept =DNE

y intercept

To find the y intercept, we have to plug x=0

f(x)=5/(0+1)

f(x)=5

y intercept =(0,5)