Answered: The functions f and g are defined by…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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The functions f and g are defined by regulations: picture
Thing in g function, tahat is barelly visible is: x<=1, (or there is only pop up cross in picture when I upload it)

Find the definition rule for a compound function g(f(x))

What does "definition" for compound functions menas? And how can I easily find it?
Please be more specific in explanation, so I can better understand the topic.

Thank you.

1
_f(x) =-
12-x |지>1°
15||
g(x)={
2-x x>1

Expert Solution

Step 1

In this question, it is given that

$f (x) = \{|x|, |x| \leq 1 2 - x^{2}, |x| > 1\}$

$g (x) = \{1, x \leq 1 2 - x, x > 1\}$

Now, we have to find g(f(x))

For that, we have to put the value of f(x) in g(x)

Step 2

We have,

$f (x) = \{|x|, |x| \leq 1 2 - x^{2}, |x| > 1\}$

$g (x) = \{1, x \leq 1 2 - x, x > 1\}$

For $x \leq 1$

g(x)=1

therefore, g(f(x))=1

For $x > 1$

$g (x) = 2 - x$

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

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