Chapter 5: Q. 3 (page 343)

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)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$

Short Answer

Expert verified

$(a) (f o g) (2) = \sqrt{11} (b) (g o f) (- 2) = 1 (c) (f o f) (4) = \sqrt{\sqrt{6} + 2} (d) (g o g) (- 1) = 19$

Step by step solution

Part (a) Step 1: Given information

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

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1$

Part(a) : Step 2:Calculate (f o g)(2)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (f o g) (2) = f (g (2) g (2) = 2 {(2)}^{2} + 1 = 9 f (9) = \sqrt{9 + 2} = \sqrt{11} (f o g) (2) = \sqrt{11}$

Part(b): Step 1: Calculate (g o f) (-2)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (g o f) (- 2) = g (f (- 2)) f (- 2) = \sqrt{- 2 + 2} = 0 g (0) = 2 {(0)}^{2} + 1 = 1 (g o f) (- 2) = 1$

Part(c) : Step 1: (f o f)(4)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (f o f) (4) = f (f (4)) f (4) = \sqrt{4 + 2} = \sqrt{6} f (\sqrt{6}) = \sqrt{\sqrt{6} + 2} (f o f) (4) = \sqrt{\sqrt{6} + 2}$

Part(d): Step 1: ( g o g) (-1)

$f (x) = \sqrt{x + 2} g (x) = 2 x^{2} + 1 (g o g) (- 1) = g (g (- 1)) g (- 1) = 2 {(- 1)}^{2} + 1 = 3 g (3) = 2 {(3)}^{2} + 1 = 19$

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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)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part(a) : Step 2:Calculate (f o g)(2)

Part(b): Step 1: Calculate (g o f) (-2)

Part(c) : Step 1: (f o f)(4)

Part(d): Step 1: ( g o g) (-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)=x+2:g(x)=2x2+1

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part(a) : Step 2:Calculate (f o g)(2)

Part(b): Step 1: Calculate (g o f) (-2)

Part(c) : Step 1: (f o f)(4)

Part(d): Step 1: ( g o g) (-1)

One App. One Place for Learning.

Most popular questions from this chapter

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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)
$f (x) = \sqrt{x + 2} : g (x) = 2 x^{2} + 1$