List the critical values of the related function. Then solve the inequality.
-$$\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$$
A) No critical values; $( - \infty , \infty )$
B) $2 ; ( - \infty , 2 ]$
C) No critical values; $\varnothing$
D) $4 ; [ 4 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$, we first find a common denominator and simplify the inequality. Both denominators are always positive for all real x, so there are no critical values from the denominators turning zero. Solving the inequality does not lead to a specific interval but shows the original inequality is always true for all x, hence the solution is $( - \infty , \infty )$.

List the Critical Values of the Related Function 2x2+1≥44x2+3\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }x2+12​≥4x2+34​

List the Critical Values of the Related Function $\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$