Q 10.4TI For聽functions聽f(x)=聽x2+1,聽an... [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 10.4TI (page 992)

$For functions f (x) = x^{2} + 1, and g (x) = 3 x 鈭� 5, find (A) (f 鈭� g) 鈳� (鈭� 1), (B) (g 鈭� f) (2), and (C) (f 鈭� f) (鈭� 1) .$

Short Answer

Expert verified

Part(a) 63

Part(b) -14

Part(c) 5

Step by step solution

Step 1. Given information

Find

f (x) = x^{2} + 1, and g (x) = 3 x 鈭� 5, find (A) (f 鈭� g) 鈳� (鈭� 1), (B) (g 鈭� f) (2), and (C) (f 鈭� f) (鈭� 1) .

Part(a)Step 2. Calculation

$\begin{array}{l} Use the definition of (f 鈭� g) (- 1) . & (f 鈭� g) (- 1) = f (g (- 1)) \\ Find g (- 1) where g (x) = 3 x - 5 . & (f 鈭� g) (- 1) = f (3 路 (- 1) - 5) \\ Simplify. & (f 鈭� g) (- 1) = f (- 8) \\ Find f (- 8) where f (x) = x^{2} + 1 . & (f 鈭� g) (- 1) = (- 8)^{2} - 1 \\ Simplify. & (f 鈭� g) (- 1) = 63 \end{array}$

Part (b) Step 3. Calculation

$\begin{array}{l} Use the definition of (g 鈭� f) (2) . & (g 鈭� f) (2) = g (f (2)) \\ Find f (2) where f (x) = x^{2} + 1 . & (g 鈭� f) (2) = g ((2)^{2} + 1) \\ Simplify. & (g 鈭� f) (2) = g (5) \\ Find g (5) where g (x) = 3 x - 5 . & (g 鈭� f) (2) = 3 (- 3) - 5 \\ Simplify. & (g 鈭� f) (2) = - 14 \end{array}$

Part(c)Step 4. Calculation

$\begin{array}{l} Use the definition of (f 鈭� f) (- 1) . & (f 鈭� f) (- 1) = f (f (- 1)) \\ Find f (2) where f (x) = x^{2} + 1 . & (f 鈭� f) (- 1) = f ({(- 1)}^{2} + 1) \\ Simplify. & (f 鈭� f) (- 1) = f (2) \\ Find f (2) where f (x) = x^{2} + 1 . & (f 鈭� f) (- 1) = 2^{2} + 1 \\ Simplify. & (f 鈭� f) (- 1) = 5 \end{array}$

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91影视

$For functions f (x) = x^{2} + 1, and g (x) = 3 x 鈭� 5, find (A) (f 鈭� g) 鈳� (鈭� 1), (B) (g 鈭� f) (2), and (C) (f 鈭� f) (鈭� 1) .$

Short Answer

Step by step solution

Step 1. Given information

Part(a)Step 2. Calculation

Part (b) Step 3. Calculation

Part(c)Step 4. Calculation

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91影视

Forfunctionsf(x)=x2+1,andg(x)=3x鈭�5,find(A)(f鈭�g)鈳�(鈭�1),(B)(g鈭�f)(2),and(C)(f鈭�f)(鈭�1).

Short Answer

Step by step solution

Step 1. Given information

Part(a)Step 2. Calculation

Part (b) Step 3. Calculation

Part(c)Step 4. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Probability and Statistics

Statistics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

$For functions f (x) = x^{2} + 1, and g (x) = 3 x 鈭� 5, find (A) (f 鈭� g) 鈳� (鈭� 1), (B) (g 鈭� f) (2), and (C) (f 鈭� f) (鈭� 1) .$