Chapter 6: Q. 48 (page 419)

find $(f \circ g) (x)$ and $(g \circ f) (x)$ and graph each of these functions.
role="math" localid="1646345864735" $f (x) = \frac{1}{2} x g (x) = 2 c s c x$

Short Answer

Expert verified

If $f (x) = \frac{1}{2} x$ and $g (x) = 2 c s c x$ then $(f \circ g) (x) = c s c (x)$ and its graph is

and $(g \circ f) (x) = 2 c s c (\frac{1}{2} x)$ and its graph is

Step by step solution

Step 1. Given data

The given functions are

$f (x) = \frac{1}{2} x g (x) = 2 c s c x$

Step 2. Composition of function

$(f \circ g) (x)$ composition of function is

role="math" localid="1646346006367" $(f \circ g) (x) = f (g (x)) (f \circ g) (x) = f (2 c s c (x)) (f \circ g) (x) = \frac{1}{2} (2 c s c (x)) (f \circ g) (x) = c s c (x)$

Step 3. Graph of (f∘g)(x)

Plot the graph of $(f \circ g) (x) = c s c (x)$

Step 4. Composition of function

$(g \circ f) (x)$ composition of function is

$(g \circ f) (x) = g (f (x)) (g \circ f) (x) = g (\frac{1}{2} x) (g \circ f) (x) = 2 c s c (\frac{1}{2} x)$

Step 5. Graph of (g∘f)(x)

Plot the graph of $(g \circ f) (x) = 2 c s c (\frac{1}{2} x)$

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find $(f \circ g) (x)$ and $(g \circ f) (x)$ and graph each of these functions.
role="math" localid="1646345864735" $f (x) = \frac{1}{2} x g (x) = 2 c s c x$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Composition of function

Step 3. Graph of (f∘g)(x)

Step 4. Composition of function

Step 5. Graph of (g∘f)(x)

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find(f∘g)(x) and (g∘f)(x)and graph each of these functions.role="math" localid="1646345864735" f(x)=12xg(x)=2cscx

Short Answer

Step by step solution

Step 1. Given data

Step 2. Composition of function

Step 3. Graph of (f∘g)(x)

Step 4. Composition of function

Step 5. Graph of (g∘f)(x)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Statistics

Probability and Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

find $(f \circ g) (x)$ and $(g \circ f) (x)$ and graph each of these functions.
role="math" localid="1646345864735" $f (x) = \frac{1}{2} x g (x) = 2 c s c x$