Question 1004118
Start with f(x) and solve for x
f(x) = 5x-2
f(x)+2 = 5x-2+2
f(x)+2 = 5x
(1/5)*(f(x)+2) = (1/5)*5x
(1/5)*(f(x)+2) = x
x = (1/5)*(f(x)+2)


Now plug this into g(x)
g(x) = x-2
g(x) = (1/5)*(f(x)+2)-2
g(x) = (1/5)*f(x)+(1/5)*2-2
g(x) = (1/5)*f(x)+2/5-2
g(x) = (1/5)*f(x)+2/5-10/5
g(x) = (1/5)*f(x)-8/5


So,
{{{g(x) = (1/5)*f(x)-8/5}}}


Description: Start with the graph of f(x). Vertically compress it by a factor of 5. Then shift everything down 8/5 = 1.6 units to get the graph of g(x).