Chapter 7: Q. 72 (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.
$h (g^{- 1} (- \frac{4}{5}))$

Short Answer

Expert verified

The required exact value of given expression is $- \frac{3}{4}$ .

Step by step solution

Step 1. Given information.

The composite function $h (g^{- 1} (- \frac{4}{5}))$ .

Step 2. Here, let g-1-45=x.

So,

$g (x) = - \frac{4}{5} \cos x = - \frac{4}{5} S i n c e, \cos x < 0, s o \frac{π}{2} \leq x \leq π Now, sinx = \sqrt{1 - \cos^{2} x} = \sqrt{1 - {(- \frac{4}{5})}^{2}} = \sqrt{1 - \frac{16}{25}} = \sqrt{\frac{9}{25}} = \frac{3}{5}$

Step 3. Now, find hg-1-45.

$h (g^{- 1} (- \frac{4}{5})) = h (x) = \tan x = \frac{\sin x}{\cos x} = \frac{3 / 5}{- 4 / 5} = \frac{- 3}{4}$

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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.
$h (g^{- 1} (- \frac{4}{5}))$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let g-1-45=x.

Step 3. Now, find hg-1-45.

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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.hg-1-45

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Here, let g-1-45=x.

Step 3. Now, find hg-1-45.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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.
$h (g^{- 1} (- \frac{4}{5}))$