Q. 64 If f(x)=ax+bcx+d;聽g(x)=mx,聽the... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 64 (page 257)

If $f (x) = \frac{a x + b}{c x + d}; g (x) = m x,$ then find: -
(a) $f 鈭� g$
(b) $g 鈭� f$
(c)Domain of $f 鈭� g$ and $g 鈭� f$ .
(d)the conditions for which $f 鈭� g = g 鈭� f$ .

Short Answer

Expert verified

(a) $f 鈭� g (x) = \frac{a m x + b}{c m x + d}$

(b) $g 鈭� f (x) = \frac{m a x + b}{c x + d}$

(c)Domain of $f 鈭� g$ is set of real numbers except $x = - \frac{d}{c}$ and domain of $g 鈭� f$ is set of real numbers.

(d) $f 鈭� g (x) = g 鈭� f (x)$ if, $m = 1 .$

Step by step solution

Given Information

Given that $f (x) = \frac{a x + b}{c x + d}; g (x) = m x .$

Part (a) Step 1 Solution

We know that $f 鈭� g (x) = f (g (x)) .$

Here, $f (x) = \frac{a x + b}{c x + d}; g (x) = m x$

Now,

$f 鈭� g (x) = f (g (x)) f 鈭� g (x) = \frac{a (g (x)) + b}{c (g (x)) + d} f 鈭� g (x) = \frac{a {m x} + b}{c {m x} + d} f 鈭� g (x) = \frac{a m x + b}{c m x + d} .$

Part (b) Step 1 Solution

We know that $g 鈭� f (x) = g (f (x)) .$

Here, $f (x) = \frac{a x + b}{c x + d}; g (x) = m x .$

Now,

$g 鈭� f (x) = m (f (x)) g 鈭� f (x) = m \{\frac{a x + b}{c x + d}\} g 鈭� f (x) = = \frac{m a x + b}{c x + d} .$

Part (C) Step 1 Solution

Domain of $f (x) = \frac{a x + b}{c x + d}$ is set of real numbers except than $x = - \frac{d}{c} .$ Domain of $g (x) = m x$ is set of real numbers. So, domain of $f 鈭� g (x)$ is set of real numbers except then $x = - \frac{d}{c} .$

Now, domain of $g 鈭� f (x)$ is set of real numbers.

Part (d) Step 1 Solution

Suppose, $f 鈭� g (x) = g 鈭� f (x)$

$\frac{a m x + b}{c m x + d} = \frac{m a x + b}{c x + d} c m x + d = c x + d$

compare both sides

$c m = c m = 1 .$

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91影视

If $f (x) = \frac{a x + b}{c x + d}; g (x) = m x,$ then find: -
(a) $f 鈭� g$
(b) $g 鈭� f$
(c)Domain of $f 鈭� g$ and $g 鈭� f$ .
(d)the conditions for which $f 鈭� g = g 鈭� f$ .

Short Answer

Step by step solution

Given Information

Part (a) Step 1 Solution

Part (b) Step 1 Solution

Part (C) Step 1 Solution

Part (d) Step 1 Solution

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91影视

If f(x)=ax+bcx+d;g(x)=mx,then find: -(a)f鈭�g(b)g鈭�f(c)Domain of f鈭�gand g鈭�f.(d)the conditions for which f鈭�g=g鈭�f.

Short Answer

Step by step solution

Given Information

Part (a) Step 1 Solution

Part (b) Step 1 Solution

Part (C) Step 1 Solution

Part (d) Step 1 Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If $f (x) = \frac{a x + b}{c x + d}; g (x) = m x,$ then find: -
(a) $f 鈭� g$
(b) $g 鈭� f$
(c)Domain of $f 鈭� g$ and $g 鈭� f$ .
(d)the conditions for which $f 鈭� g = g 鈭� f$ .