Chapter 7: Q. 75 (page 458)

In Problems 67–78, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π and h (x) = tanx, - \frac{π}{2} < x < \frac{π}{2}$
Find the exact value of each composite function.
role="math" localid="1646619716494" $g^{- 1} (f (- \frac{4 π}{3}))$

Short Answer

Expert verified

The required exact value of given expression is $\frac{π}{6}$ .

Step by step solution

Step 1. Given information.

The composite function $g^{- 1} (f (- \frac{4 π}{3}))$ .

Step 2. Calculate f-4π3.

$f (- \frac{4 π}{3}) = \sin (- \frac{4 π}{3}) = \frac{\sqrt{3}}{2}$

Step 3. Now, find g-1f-4π3.

$g^{- 1} (f (- \frac{4 π}{3})) = g^{- 1} (\frac{\sqrt{3}}{2}) L e t, g^{- 1} (\frac{\sqrt{3}}{2}) = x g (x) = \frac{\sqrt{3}}{2} \cos x = \frac{\sqrt{3}}{2} \sin c e, \cos x = \frac{\sqrt{3}}{2} f o r x = \frac{π}{6} o n t h e i n t e r v a l 0 \leq x \leq π . So, g^{- 1} (f (- \frac{4 π}{3})) = x = \frac{π}{6}$

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In Problems 67–78, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π and h (x) = tanx, - \frac{π}{2} < x < \frac{π}{2}$
Find the exact value of each composite function.
role="math" localid="1646619716494" $g^{- 1} (f (- \frac{4 π}{3}))$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate f-4π3.

Step 3. Now, find g-1f-4π3.

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In Problems 67–78,fx=sinx,-π2≤x≤π2,gx=cosx,0≤x≤πandhx=tanx,-π2<x<π2Find the exact value of each composite function.role="math" localid="1646619716494" g-1f-4π3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate f-4π3.

Step 3. Now, find g-1f-4π3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

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Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 67–78, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π and h (x) = tanx, - \frac{π}{2} < x < \frac{π}{2}$
Find the exact value of each composite function.
role="math" localid="1646619716494" $g^{- 1} (f (- \frac{4 π}{3}))$