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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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