Q. 8 For the function f defined by f(... [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 3: Q. 8 (page 176)

For the function f defined by $f (x) = x^{2} - 4 x + 1$ , find:
(a) f(2)
(b) f(x) + f(2)
(c) f(-x)
(d) -f(x)
(e) f(x + 2)
(f) $\frac{f (x + h) - f (x)}{h}, h 鈮� 0$

Short Answer

Expert verified

(a) $f (2) = - 3$

(b) $f (x) + f (2) = x^{2} - 4 x - 2$

(d) $- f (x) = - x^{2} + 4 x - 1$

(e) $f (x + 2) = x^{2} - 3$

(f) $\frac{f (x + h) - f (x)}{h} = 2 x + h - 4, h 鈮� 0$

Step by step solution

Part (a) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (a) Step 2. Calculation

Now, $f (2) = 2^{2} - 4.2 + 1$

$= - 3$

Part (b) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (b) Step 2. Calculation

$f (x) + f (2) = x^{2} - 4 x + 1 - 3$

$= x^{2} - 4 x - 2$

Part (c) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (c) Step 2. Calculation

$f (- x) = {(- x)}^{2} - 4 (- x) + 1$

role="math" localid="1647455449353" $= x^{2} + 4 x + 1$

Part (d) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (d) Step 2. Calculation

$- f (x) = - x^{2} + 4 x - 1$

Part (e) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (e) Step 2. Calculation

$f (x + 2) = {(x + 2)}^{2} - 4 (x + 2) + 1$

$= x^{2} + 4 x + 4 - 4 x - 8 + 1$

$= x^{2} - 3$

Part (f) Step 1. Given Information

$f (x) = x^{2} - 4 x + 1$

Part (f) Step 2.Calculation

$\frac{f (x + h) - f (x)}{h} = \frac{{{(x + h)}^{2} - 4 (x + h) + 1} - {x^{2} - 4 x + 1}}{h}, h 鈮� 0$

$= \frac{x^{2} + 2 x h + h^{2} - 4 x - 4 h + 1 - x^{2} + 4 x - 1}{h}$

$= \frac{h (2 x - 4 + h)}{h}$

$= 2 x + h - 4$

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x	$y = f (x)$
-2	0
-1	1
0	4
1	9
2	16

91影视

For the function f defined by $f (x) = x^{2} - 4 x + 1$ , find:
(a) f(2)
(b) f(x) + f(2)
(c) f(-x)
(d) -f(x)
(e) f(x + 2)
(f) $\frac{f (x + h) - f (x)}{h}, h 鈮� 0$

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Calculation

Part (b) Step 1. Given Information

Part (b) Step 2. Calculation

Part (c) Step 1. Given Information

Part (c) Step 2. Calculation

Part (d) Step 1. Given Information

Part (d) Step 2. Calculation

Part (e) Step 1. Given Information

Part (e) Step 2. Calculation

Part (f) Step 1. Given Information

Part (f) Step 2.Calculation

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91影视

For the function f defined by f(x)=x2-4x+1, find:(a) f(2)(b) f(x) + f(2)(c) f(-x)(d) -f(x)(e) f(x + 2)(f)f(x+h)-f(x)h,h鈮�0

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Calculation

Part (b) Step 1. Given Information

Part (b) Step 2. Calculation

Part (c) Step 1. Given Information

Part (c) Step 2. Calculation

Part (d) Step 1. Given Information

Part (d) Step 2. Calculation

Part (e) Step 1. Given Information

Part (e) Step 2. Calculation

Part (f) Step 1. Given Information

Part (f) Step 2.Calculation

One App. One Place for Learning.

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For the function f defined by $f (x) = x^{2} - 4 x + 1$ , find:
(a) f(2)
(b) f(x) + f(2)
(c) f(-x)
(d) -f(x)
(e) f(x + 2)
(f) $\frac{f (x + h) - f (x)}{h}, h 鈮� 0$