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

SOLUTION: Find the domain and range of the function f(x) = (ln(1 - x^2))/√(2x^2 + x - 3).

Question 1183958: Find the domain and range of the function f(x) = (ln(1 - x^2))/√(2x^2 + x - 3).
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The allowable x values for are {x ∈ R| 1 > x^2}, or {x ∈ R| 1 > x > -1}, or the open interval (-1,1).
The allowable x values for are those for which , i.e., the interval (, -3/2) ∪ (1, ).

The domain of f(x) would be the intersection of the allowable x values for the top and bottom functions.

That is, (-1,1) ∩ {(, -3/2) ∪ (1, )} = ∅, the empty set.

Therefore, the domain of the function is the empty set, and consequently the range will be the empty set, too.

NOTE: In practical terms you can actually verify this fact.
The Desmos and Symbolab online graphing utilities will give you an "empty" graph for this function,
that is, all you will see is the x-y coordinate system, and its graph doesn't exist.

RELATED QUESTIONS
Find the domain, range, intercepts, and asymptote of the function:... (answered by lwsshak3)

State the domain and range of each function.... g(x)=ln(2x-1)... (answered by jsmallt9)

What is the domain and range of f(x)=... (answered by solver91311,MathLover1)

Given : f(x)=2x^2+2 1. Find the domain of f(x). 2. Find the range of... (answered by josgarithmetic)

How do I find the Domain and range of this function? f(x)=2x^2 - x... (answered by solver91311)

Find the domain and range of the function... (answered by Fombitz)

Find the domain and range of the function f(x) = (x^2 + 1)/( 4x^2 - 8x +... (answered by MathLover1)

Find the domain of the function f(x) = ln... (answered by ikleyn)

Find the domain and range of the function. 1.f(x)= 3sinx 2.f(x)= 2/x-1 (answered by lwsshak3)