Chapter 10: Q. 10.3 (page 992)

For functions $f (x) = x^{2} - 9$ and
$g (x) = 2 x + 5$ , find
$(f \circ g) (- 2)$
$(g \circ f) (- 3)$
$(f \circ f) (4)$

Short Answer

Expert verified

Part a. $(f \circ g) (- 2) = - 8$

Part b. $(g \circ f) (- 3) = 5$

Part c. $(f \circ f) (4) = 40$

Step by step solution

Part (a) Step 1. Find (f∘g)(-2)

Using the definition of composition of functions we have $(f \circ g) (- 2) = f (g (- 2))$ .

Find $g (- 2)$ where $g (x) = 2 x + 5$ .

$(f \circ g) (- 2) = f (2 \cdot (- 2) + 5) (f \circ g) (- 2) = f (- 4 + 5) (f \circ g) (- 2) = f (1)$

Find $f (1)$ where $f (x) = x^{2} - 9$

$(f \circ g) (- 2) = 1^{2} - 9 (f \circ g) (- 2) = 1 - 9 (f \circ g) (- 2) = - 8$

Part (b) Step 1. Find (g∘f)(-3)

Using the definition of composition of functions we have $(g \circ f) (- 3) = g (f (- 3))$

Find $f (- 3)$ where $f (x) = x^{2} - 9$ .

$(g \circ f) (- 3) = g ({(- 3)}^{2} - 9) (g \circ f) (- 3) = g (9 - 9) (g \circ f) (- 3) = g (0)$

Find $g (0)$ where $g (x) = 2 x + 5$

$(g \circ f) (- 3) = 2 \cdot 0 + 5 (g \circ f) (- 3) = 0 + 5 (g \circ f) (- 3) = 5$

Part (c) Step 1. Find (f∘f)(4)

Using the definition of composition of functions we have $(f \circ f) (4) = f (f (4))$ .

Find $f (4)$ where $f (x) = x^{2} - 9$

$(f \circ f) (4) = f (4^{2} - 9) (f \circ f) (4) = f (16 - 9) (f \circ f) (4) = f (7)$

Now find $f (7)$ where $f (x) = x^{2} - 9$ .

$(f \circ f) (4) = 7^{2} - 9 (f \circ f) (4) = 49 - 9 (f \circ f) (4) = 40$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For functions $f (x) = x^{2} - 9$ and
$g (x) = 2 x + 5$ , find
$(f \circ g) (- 2)$
$(g \circ f) (- 3)$
$(f \circ f) (4)$

Short Answer

Step by step solution

Part (a) Step 1. Find (f∘g)(-2)

Part (b) Step 1. Find (g∘f)(-3)

Part (c) Step 1. Find (f∘f)(4)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Applied Mathematics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

For functions f(x)=x2-9and g(x)=2x+5, find(f∘g)(-2)(g∘f)(-3)(f∘f)(4)

Short Answer

Step by step solution

Part (a) Step 1. Find (f∘g)(-2)

Part (b) Step 1. Find (g∘f)(-3)

Part (c) Step 1. Find (f∘f)(4)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Applied Mathematics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

For functions $f (x) = x^{2} - 9$ and
$g (x) = 2 x + 5$ , find
$(f \circ g) (- 2)$
$(g \circ f) (- 3)$
$(f \circ f) (4)$