Q. 10.13 Verify that the functions are in... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 10.13 (page 999)

Verify that the functions are inverse functions. $f (x) = 4 x 鈭� 3 and g (x) = \frac{x + 3}{4} .$

Short Answer

Expert verified

Since both g(f(x)) = x and f(g(x)) = x are true ,the functions f(x)=4x-3 and g(x)= $\frac{x + 3}{4}$ are inverse functions. That is, they are inverses of each other.

Step by step solution

Step 1. Given information

The given equation are $f (x) = 4 x 鈭� 3 and g (x) = \frac{x + 3}{4} .$

Step 2. Checking for the equation first

The functions are inverses of each other if g(f(x)= x and f(g(x) = x.

$Subsitute 4 x - 3 for f (x) g (4 x - 3) = ? Find g (4 x - 3) where g (x) = \frac{x + 3}{4} \frac{4 x - 3 + 3}{4} = \frac{4 x}{4} = x = x$

Step 3. Checking for the equation second

$Substitute \frac{x + 3}{4} for g (x) . f (\frac{x + 3}{4}) = x Find f (\frac{x + 3}{4}) for f (x) = 4 x - 3 4 (\frac{x + 3}{4}) - 3 = x + 3 - 3 = x$

Since both g(f(x)) = x and f(g(x)) = x are true ,the functions f(x)=4x-3 and g(x)= $\frac{x + 3}{4}$ are inverse functions. That is, they are inverses of each other.

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91影视

Verify that the functions are inverse functions. $f (x) = 4 x 鈭� 3 and g (x) = \frac{x + 3}{4} .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Checking for the equation first

Step 3. Checking for the equation second

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91影视

Verify that the functions are inverse functions.f(x)=4x鈭�3andg(x)=x+34.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Checking for the equation first

Step 3. Checking for the equation second

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Verify that the functions are inverse functions. $f (x) = 4 x 鈭� 3 and g (x) = \frac{x + 3}{4} .$