Solve f*f-2-2≥15

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for f

f \in (- \infty, - 19] \cup [19, + \infty)

Evaluate

f \times f - 2 - 2 \geq 15

Simplify

More Steps

f^{2} - 4 \geq 15

Move the expression to the left side

f^{2} - 4 - 15 \geq 0

Subtract the numbers

f^{2} - 19 \geq 0

Rewrite the expression

f^{2} - 19 = 0

Move the constant to the right-hand side and change its sign

f^{2} = 0 + 19

Removing 0 doesn't change the value,so remove it from the expression

f^{2} = 19

Take the root of both sides of the equation and remember to use both positive and negative roots

f = \pm 19

Separate the equation into 2 possible cases

f = 19 f = - 19

Determine the test intervals using the critical values

f < - 19 - 19 < f < 19 f > 19

Choose a value form each interval

f_{1} = - 5 f_{2} = 0 f_{3} = 5

To determine if f < - 19 is the solution to the inequality,test if the chosen value f = - 5 satisfies the initial inequality

More Steps

f < - 19 is the solution f_{2} = 0 f_{3} = 5

To determine if - 19 < f < 19 is the solution to the inequality,test if the chosen value f = 0 satisfies the initial inequality

More Steps

f < - 19 is the solution - 19 < f < 19 is not a solution f_{3} = 5

To determine if f > 19 is the solution to the inequality,test if the chosen value f = 5 satisfies the initial inequality

More Steps

f < - 19 is the solution - 19 < f < 19 is not a solution f > 19 is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

f \leq - 19 is the solution f \geq 19 is the solution

Solution

f \in (- \infty, - 19] \cup [19, + \infty)

Show Solution