Chapter 2: Q. 9 (page 126)

For the functions $f (x) = 2 x^{2} + 1$ and $g (x) = 3 x - 2$ , find
the following and simplify:
(a) $f - g$
(b) $f \cdot g$
(c) $f (x + h) - f (x)$

Short Answer

Expert verified

For functions $f (x) = 2 x^{2} + 1 g (x) = 3 x - 2$

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

(b) $(f \cdot g) (x) = 6 x^{3} - 4 x^{2} + 3 x - 2$

Step by step solution

Step 1. given data

The given functions are

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

Step 2. Part (a)

The difference of function $f (x) & g (x)$ is

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

Step 3. Part (b)

The product of functions $f (x) & g (x)$ is

$(f \cdot g) (x) = f (x) \cdot g (x) (f \cdot g) (x) = (2 x^{2} + 1) (3 x - 2) (f \cdot g) (x) = (2 x^{2}) (3 x) - (2 x^{2}) (2) + (1) (3 x) - (1) (2) (f \cdot g) (x) = 6 x^{3} - 4 x^{2} + 3 x - 2$

Step 4. Part (c)

Substitute $x + h$ for x in the function $f (x)$

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

sorole="math" localid="1645903721224" $f (x + h) - f (x) = (2 x^{2} + 4 x h + 2 h^{2} + 1) - (2 x^{2} + 1) f (x + h) - f (x) = 2 x^{2} + 4 x h + 2 h^{2} + 1 - 2 x^{2} - 1 f (x + h) - f (x) = 4 x h + 2 h^{2}$

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For the functions $f (x) = 2 x^{2} + 1$ and $g (x) = 3 x - 2$ , find
the following and simplify:
(a) $f - g$
(b) $f \cdot g$
(c) $f (x + h) - f (x)$

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 3. Part (b)

Step 4. Part (c)

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For the functions f(x)=2x2+1and g(x)=3x-2, findthe following and simplify:(a) f-g(b) f·g(c) f(x+h)-f(x)

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 3. Part (b)

Step 4. Part (c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

For the functions $f (x) = 2 x^{2} + 1$ and $g (x) = 3 x - 2$ , find
the following and simplify:
(a) $f - g$
(b) $f \cdot g$
(c) $f (x + h) - f (x)$