Chapter 7: Q 70. (page 458)

In problem, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π$ and $h (x) = \tan x, - \frac{π}{2} \leq x \leq \frac{π}{2}$ . Find the value of the composite function.
$\begin{array}{rcl} f^{- 1} (g (\frac{5 π}{6})) \end{array}$

Short Answer

Expert verified

Value of the composite function is $- \frac{π}{3}$ .

Step by step solution

Step 1. Given information

$f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π$ and $h (x) = \tan x, - \frac{π}{2} \leq x \leq \frac{π}{2}$

Step 2. Value of the composite function.

It is given that $g (x) = \cos x$ .

width="157">g5π6=cos5π6=cosπ-π6=-cosπ6=-32

$\begin{array}{rcl} f^{- 1} (g (\frac{5 π}{6})) & = & f^{- 1} (- \frac{\sqrt{3}}{2}) \\ = & \sin^{- 1} (- \frac{\sqrt{3}}{2}) \end{array}$

Let .

$\begin{array}{rcl} \sin y & = & - \frac{\sqrt{3}}{2} \\ = & - \sin (\frac{π}{3}) \\ = & \sin (- \frac{π}{3}) \end{array}$

So,

localid="1647840234802" $\begin{array}{rcl} f^{- 1} (g (\frac{5 π}{6})) & = & - \frac{π}{3} \end{array}$

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In problem, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π$ and $h (x) = \tan x, - \frac{π}{2} \leq x \leq \frac{π}{2}$ . Find the value of the composite function.
$\begin{array}{rcl} f^{- 1} (g (\frac{5 π}{6})) \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the composite function.

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In problem, f(x)=sinx,-π2≤x≤π2,g(x)=cosx,0≤x≤πand h(x)=tanx,-π2≤x≤π2. Find the value of the composite function. f-1g5π6

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the composite function.

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 problem, $f (x) = \sin x, - \frac{π}{2} \leq x \leq \frac{π}{2}, g (x) = \cos x, 0 \leq x \leq π$ and $h (x) = \tan x, - \frac{π}{2} \leq x \leq \frac{π}{2}$ . Find the value of the composite function.
$\begin{array}{rcl} f^{- 1} (g (\frac{5 π}{6})) \end{array}$