Chapter 11: Q. 278 (page 1069)

For the function $f (x) = x + 2$ and $g (x) = 3 x^{2} - 2 x + 4$ find (a) $(f \cdot g) (x)$
(b) $(f \cdot g) (- 1)$

Short Answer

Expert verified

The solution is (a) $3 x^{3} + 4 x^{2} + 8$

(b)The value at x=-1 is $9$

Step by step solution

Step 1. Given information

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

Part (a) Step 1. Finding (f.g)(x)

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

Part (b) Step 1. Substitute x = -1

$(f \cdot g) (x) = 3 x^{3} + 4 x^{2} + 8 (f \cdot g) (- 1) = 3 {(- 1)}^{3} + 4 {(- 1)}^{2} + 8 = 9$

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For the function $f (x) = x + 2$ and $g (x) = 3 x^{2} - 2 x + 4$ find (a) $(f \cdot g) (x)$
(b) $(f \cdot g) (- 1)$

Short Answer

Step by step solution

Step 1. Given information

Part (a) Step 1. Finding (f.g)(x)

Part (b) Step 1. Substitute x = -1

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For the function fx=x+2and gx=3x2-2x+4find (a) f·gx(b)f·g-1

Short Answer

Step by step solution

Step 1. Given information

Part (a) Step 1. Finding (f.g)(x)

Part (b) Step 1. Substitute x = -1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

For the function $f (x) = x + 2$ and $g (x) = 3 x^{2} - 2 x + 4$ find (a) $(f \cdot g) (x)$
(b) $(f \cdot g) (- 1)$