SOLUTION: Find the domain and range of f(x)=x^2 Find the domain and range of f(x)=1/(x^2-1)^1/2 Find the domain and range of f(x)=x^2

Algebra ->  Functions -> SOLUTION: Find the domain and range of f(x)=x^2 Find the domain and range of f(x)=1/(x^2-1)^1/2 Find the domain and range of f(x)=x^2      Log On


   

Question 121381: Find the domain and range of f(x)=x^2
Find the domain and range of f(x)=1/(x^2-1)^1/2
Find the domain and range of f(x)=x^2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E2
There are no restrictions on domain.
The domain is (-infinity,infinity).
Since the value of x is squared, f(x) will always be equal or greater than 0.
The range is [0,infinity).
The bracket, [, means includes 0 in this definition.
f%28x%29=1%2F%28%28x%5E2-1%29%5E%281%2F2%29%29
There are several restrictions on the domain.
The function is not defined when the denominator equals zero.
Therefore x cannot equal 1 or -1.
The square root also requires a positive value.
x%5E2-1%3E0
x%5E2%3E1
x%3E1 and x%3C-1

Since the output of the square root function is also always positive,
the range is also positive.
As x grows large, either negative or positive, f(x) goes to zero.
The range is (0,infinity).