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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 75 (page 458)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

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

02

Step 2. Calculate f-4π3.

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

03

Step 3. Now, find g-1f-4π3.

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

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