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(d) Use function notation to write g in terms of f.
1. g(x) = (x − 10)2
f(x)= x2
answer: g(x)= f(____)
2. g(x)= -x3-2
f(x)= x3
answer: g(x)= -f(____) + (____)
3. g(x)= -(x+6)2+2
f(x)= x2
answer: g(x)= -f(____) + (____)
4. g(x) = (x + 2)3 − 8
f(x)= x2
answer: g(x)= f(____) + (____)
5. g(x) = 8 − |x + 4|
f(x)= |x|
answer: g(x)= ____ - f(____)
6. g(x) = |−x + 5| + 7
f(x)= |x|
answer: g(x)= f(____) + (____)
7.

f(x)= √x
answer: g(x)= f(____) + (____)

Sagot :

The value of g in terms of f is:

[tex]x^{4} -20x^{2} +100[/tex]

[tex]x^{9} -2[/tex]

[tex]-x^{4} -12x^{2} -34[/tex]

[tex]8-||X|+4|[/tex]

[tex]|-|x|+5|+7[/tex]

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Finding g in terms of f, given:

g(x)=[tex]x-10^{2}[/tex],f(x)= [tex]x^{2}[/tex]

g(x)=g(f(x))

f(x)=    [tex]x^{2}[/tex] =g(  [tex]x^{2}[/tex])

g(  [tex]x^{2}[/tex]): [tex](x^{2} -10)^{2}[/tex]

Expanding [tex](x^{2} -10)^{2}[/tex] : [tex]x^{4} -20x^{2} +100[/tex]

Finding g in terms of f, given:

g(x)=[tex]-x^{3} -2[/tex],f(x)= [tex]x^{3}[/tex]

g(x)=g(f(x))

f(x)=    [tex]x^{3}[/tex] =g(  [tex]x^{3}[/tex])

g(  [tex]x^{3}[/tex]): [tex]x^{9} -2[/tex]

Finding g in terms of f, given:

g(x)=[tex]-(x-6)^{2} +2[/tex] ,f(x)= [tex]x^{2}[/tex]

g(x)=g(f(x))

f(x)=    [tex]x^{2}[/tex] =g(  [tex]x^{2}[/tex])

g(  [tex]x^{2}[/tex]): [tex]-x^{4} -12x^{2} -34[/tex]

Finding g in terms of f, given:

g(x)=[tex]8-|x+4|[/tex] ,f(x)= [tex]|x|[/tex]

g(x)=g(f(x))

f(x)=    [tex]|x|[/tex] =g(  [tex]|x|[/tex] )

g(  [tex]|x|[/tex] ): [tex]8-||X|+4|[/tex]

Finding g in terms of f, given:

g(x)=[tex]|-x+5|[/tex] ,f(x)= [tex]|x|[/tex]

g(x)=g(f(x))

f(x)=    [tex]|x|[/tex] =g(  [tex]|x|[/tex] )

g(  [tex]|x|[/tex] ): [tex]|-|x|+5|+7[/tex]

[tex]|-|x|+5|+7[/tex]

To learn more about functions visit: brainly.com/question/14418346

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