Q.370. Given functions fx=4x3-3x2+x-1聽... [FREE SOLUTION]

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Intermediate Algebra

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ISBN: 9780998625720

Chapter 5: Q.370. (page 559)

Given functions $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$

Short Answer

Expert verified

Part (a). The solution is $12 x^{3} - 3 x^{2} + x - 2$ .

Part (b). The solution is $298$ .

Part (c). The solution is $- 4 x^{3} - 3 x^{2} + x$ .

Part (d). The solution is $18$ .

Step by step solution

Part (a) Step 1. Given information.

The given polynomial functions $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .

Part (a) Step 2. Simplify the polynomial.

$(f + g) (x) = (4 x^{3} - 3 x^{2} + x - 1) + (8 x^{3} - 1) (f + g) (x) = 4 x^{3} + 8 x^{3} - 3 x^{2} + x - 1 - 1 (f + g) (x) = 12 x^{3} - 3 x^{2} + x - 2$

Part (a) Step 3. Simplified answer.

Hence, the simplified polynomial is $(f + g) (x) = 12 x^{3} - 3 x^{2} + x - 2$ .

Part (b) Step 1. Given information.

The given functions are $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .

Part (b) Step 2. Simplify the polynomial by substituting x=3 in f+gx=12x3-3x2+x-2.

$(f + g) (3) = 12 {(3)}^{3} - 3 {(3)}^{2} + 3 - 2 (f + g) (3) = 12 脳 27 - 3 脳 9 + 3 - 2 (f + g) (3) = 324 - 27 + 3 - 2 (f + g) (3) = 327 - 29 (f + g) (3) = 298$

Part (b) Step 3. Simplified answer.

Hence, the simplified expression is $298$ .

Part (c) Step 1. Given information.

The given functions are $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .

Part (c) Step 2. Simplify the polynomial.

$(f - g) (x) = (4 x^{3} - 3 x^{2} + x - 1) - (8 x^{3} - 1) (f - g) (x) = 4 x^{3} - 8 x^{3} - 3 x^{2} + x - 1 + 1 (f - g) (x) = - 4 x^{3} - 3 x^{2} + x$

Part (c) Step 3. Simplified answer.

Hence, the simplified polynomial is $(f - g) (x) = - 4 x^{3} - 3 x^{2} + x$ .

Part (d) Step 1. Given information.

The given functions are $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .

Part (d) Step 2. Simplify the polynomial by substituting x=-2 in f-gx=-4x3-3x2+x.

$(f - g) (- 2) = - 4 {(- 2)}^{3} - 3 {(- 2)}^{2} + (- 2) (f - g) (- 2) = - 4 (- 8) - 3 (4) - 2 (f - g) (- 2) = 32 - 12 - 2 (f - g) (- 2) = 32 - 14 (f - g) (- 2) = 18$

Part (d) Step 3. Simplified answer.

Hence, the simplified solution is $18$ .

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91影视

Given functions $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Simplify the polynomial.

Part (a) Step 3. Simplified answer.

Part (b) Step 1. Given information.

Part (b) Step 2. Simplify the polynomial by substituting x=3 in f+gx=12x3-3x2+x-2.

Part (b) Step 3. Simplified answer.

Part (c) Step 1. Given information.

Part (c) Step 2. Simplify the polynomial.

Part (c) Step 3. Simplified answer.

Part (d) Step 1. Given information.

Part (d) Step 2. Simplify the polynomial by substituting x=-2 in f-gx=-4x3-3x2+x.

Part (d) Step 3. Simplified answer.

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91影视

Given functions fx=4x3-3x2+x-1and gx=8x3-1.Find (a)f+gx(b)f+g3(c)f-gx(d)f-g-2

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Simplify the polynomial.

Part (a) Step 3. Simplified answer.

Part (b) Step 1. Given information.

Part (b) Step 2. Simplify the polynomial by substituting x=3 in f+gx=12x3-3x2+x-2.

Part (b) Step 3. Simplified answer.

Part (c) Step 1. Given information.

Part (c) Step 2. Simplify the polynomial.

Part (c) Step 3. Simplified answer.

Part (d) Step 1. Given information.

Part (d) Step 2. Simplify the polynomial by substituting x=-2 in f-gx=-4x3-3x2+x.

Part (d) Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Geometry

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Given functions $f (x) = 4 x^{3} - 3 x^{2} + x - 1$ and $g (x) = 8 x^{3} - 1$ .
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$