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) $\frac{f (x + h) - f (x)}{h}, h \neq 0$

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

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

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

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

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

$= 2 x + h - 4$

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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) $\frac{f (x + h) - f (x)}{h}, h \neq 0$

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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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≠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.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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) $\frac{f (x + h) - f (x)}{h}, h \neq 0$