Chapter 7: Q. 97 (page 466)

$f (x) = 4 \tan x$
(a) Solve $f (x) = - 4$ . '
(b) For what values of x is $f (x) < - 4$ on the interval $(- \frac{π}{2}, \frac{π}{2})$ .

Short Answer

Expert verified

(a) The solution is $\{x | x = - \frac{π}{4} + n π, n is an integer\}$ .

(b) The solution set is $\{- \frac{π}{2}, - \frac{π}{4}\}$ .

Step by step solution

Step 1. Given Information

$f (x) = 4 \tan x$

(a) Solve $f (x) = - 4$ . '

(b) For what values of x is $f (x) < - 4$ on the interval $(- \frac{π}{2}, \frac{π}{2})$ .

Part (a) Step 1. The given equation is f(x)=4tanx

Putting $f (x) = - 4$

$- 4 = 4 \tan x$

Divide by 4 on both side

$- \frac{4}{4} = \frac{4}{4} \tan x - 1 = \tan x \tan x = - 1$

Part (a) Step 2. The solution for f(x)=-4.

$θ = - \frac{π}{4}$

The solution is $\{x | x = - \frac{π}{4} + n π, n is an integer\}$ .

Step (b) Part 1. The values of x is f(x)<-4 on the interval -π2,π2.

$θ = - \frac{π}{2}, - \frac{π}{4}$

The solution set is $\{- \frac{π}{2}, - \frac{π}{4}\}$

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$f (x) = 4 \tan x$
(a) Solve $f (x) = - 4$ . '
(b) For what values of x is $f (x) < - 4$ on the interval $(- \frac{π}{2}, \frac{π}{2})$ .

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given equation is f(x)=4tanx

Part (a) Step 2. The solution for f(x)=-4.

Step (b) Part 1. The values of x is f(x)<-4 on the interval -π2,π2.

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f(x)=4tanx(a) Solve f(x)=-4. '(b) For what values of x is f(x)<-4on the interval-π2,π2.

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given equation is f(x)=4tanx

Part (a) Step 2. The solution for f(x)=-4.

Step (b) Part 1. The values of x is f(x)<-4 on the interval -π2,π2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

$f (x) = 4 \tan x$
(a) Solve $f (x) = - 4$ . '
(b) For what values of x is $f (x) < - 4$ on the interval $(- \frac{π}{2}, \frac{π}{2})$ .