Chapter 5: Q. 2 (page 348)

In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = 3 x - 5; g (x) = 1 - 2 x^{2}$

Short Answer

Expert verified

(a) (f o g)(2)=-26

(b) (g o f) (-2) = -241

(d) ( g o g) (-1) = -1

Step by step solution

Given Information

We are given with two functions f(x) and g(x)

$f (x) = 3 x - 5; g (x) = 1 - 2 x^{2}$

Part(a) : Step 1: composition

$(f o g) (2) = f (g (2)) g (x) = 1 - 2 x^{2} g (2) = 1 - 2 {(2)}^{2} = - 7 f (- 7) = 3 (- 7) - 5 = - 26 (f o g) (2) = f (g (2)) = f (- 7) = - 26$

Part(b) : Step 1: composition

$f (x) = 3 x - 5; g (x) = 1 - 2 x^{2} (g o f) (- 2) = g (f (- 2)) f (- 2) = 3 (- 2) - 5 = - 11 g (- 11) = 1 - 2 {(- 11)}^{2} = - 241 (g o f) (- 2) = - 241$

Part(c) : Step 1: composition of functions

$(f o f) (4) = f (f (4)) f (x) = 3 x - 5 f (4) = 3 (4) - 5 = 7 f (7) = 3 (7) - 5 = 16 (f o f) (4) = 16$

Part(d) : Step 1: composition of functions

$(g o g) (- 1) = g (g (- 1)) g (x) = 1 - 2 x^{2} g (- 1) = 1 - 2 {(- 1)}^{2} = - 1 (g o g) (- 1) = - 1$

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In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = 3 x - 5; g (x) = 1 - 2 x^{2}$

Short Answer

Step by step solution

Given Information

Part(a) : Step 1: composition

Part(b) : Step 1: composition

Part(c) : Step 1: composition of functions

Part(d) : Step 1: composition of functions

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In Problems 2 – 4, for the given functions f and g find:(a) (f o g)(2)(b) (g o f) (-2)(c) (f o f)(4)(d) ( g o g) (-1)f(x)=3x-5;g(x)=1-2x2

Short Answer

Step by step solution

Given Information

Part(a) : Step 1: composition

Part(b) : Step 1: composition

Part(c) : Step 1: composition of functions

Part(d) : Step 1: composition of functions

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = 3 x - 5; g (x) = 1 - 2 x^{2}$