Answer :
The function f(g(x)) = 6/(6 - 7x) and g(f(x)) = 6(x - 7)/x
f(x)=x/x-7 and g(x)=6/x
a) Let's first find f(g(x)), substitute the value of g(x) into the variable x.
⇒ f(g(x)) = [tex]\frac{\frac{6}{x} }{\frac{6}{x} - 7 }[/tex]
⇒ f(g(x)) = [tex]\frac{\frac{6}{x} }{\frac{(6 - 7x)}{x} }[/tex]
⇒ f(g(x)) = [tex]\frac{6}{(6 - 7x)}[/tex]
⇒ f(g(x)) = 6/(6 - 7x)
b) Let's now find the g(f(x)), substitute the value of f(x) into the variable x.
⇒ g(f(x)) = [tex]\frac{6}{\frac{x}{(x - 7} }[/tex]
⇒ g(f(x)) = [tex]\frac{6(x - 7)}{x}[/tex]
⇒ g(f(x)) = 6(x - 7)/x
Hence, f(g(x)) = 6/(6 - 7x) and g(f(x)) = 6(x - 7)/x
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Question: Let f(x)=x/x-7 and g(x)=6/x
Find the following functions:
a) f(g(x))
b) g(f(x))
Simplify your answers.