Answer:
f(1/x) = (7x+3)/(2x+6)
g(x-2) = √(x² -13x +22)
Step-by-step explanation:
Given equations for f(x) and g(x), you want to find simplified equations for f(1/x) and g(x-2).
F(1/x)
Substituting the argument for the variable, we have ...
[tex]f\left(\dfrac{1}{x}\right)=\dfrac{3\cdot\dfrac{1}{x}+7}{6\cdot\dfrac{1}{x}+2}\\\\\boxed{f\left(\dfrac{1}{x}\right)=\dfrac{7x+3}{2x+6}}[/tex]
G(x-2)
Substituting the argument for the variable, we have ...
[tex]g(x-2)=\sqrt{(x-2)^2-9(x-2)}=\sqrt{x^2-4x+4-9x+18}\\\\\boxed{g(x-2)=\sqrt{x^2-13x+22}}[/tex]
