Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 74 (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.
$f (h^{- 1} (\frac{5}{12}))$

Short Answer

Expert verified

The required exact value of given expression is $\frac{5}{13}$ .

Step by step solution

Step 1. Given information.

The composite function $f (h^{- 1} (\frac{5}{12}))$ .

Step 2. Here, let h-1512=x.

So,

$h (x) = \frac{5}{12} \tan x = \frac{5}{12} G i v e n t h a t - \frac{蟺}{2} < x < \frac{蟺}{2} \sin c e, \tan x > 0, s o 0 < x < \frac{蟺}{2} N o w, c o t x = \frac{12}{5} \cos e c x = \sqrt{1 + c o t^{2} x} = \sqrt{1 + {(\frac{12}{5})}^{2}} = \sqrt{1 + \frac{144}{25}} = \sqrt{\frac{169}{25}} = \frac{13}{5}$

Step 3. Now, find fh-1512.

$f (h^{- 1} (\frac{5}{12})) = f (x) = \sin x = \frac{1}{\cos e c x} = \frac{1}{13 / 5} = \frac{5}{13}$

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91影视

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.
$f (h^{- 1} (\frac{5}{12}))$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let h-1512=x.

Step 3. Now, find fh-1512.

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91影视

In Problems 67鈥�78,fx=sinx,-蟺2鈮�x鈮�蟺2,gx=cosx,0鈮�x鈮�蟺andhx=tanx,-蟺2<x<蟺2Find the exact value of each composite function.fh-1512

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let h-1512=x.

Step 3. Now, find fh-1512.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

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.
$f (h^{- 1} (\frac{5}{12}))$