Chapter 7: Q. 73 (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.
$g (h^{- 1} (\frac{12}{5}))$

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

Step 2. Here, let h-1125=x

So,

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

Step 3. Now, find gh-1125.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let h-1125=x

Step 3. Now, find gh-1125.

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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.gh-1125

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let h-1125=x

Step 3. Now, find gh-1125.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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