Question

Please help and explain because I'm confused.

Answer 1

First, find where they are equal
because g(x) grows at a faster rate so it will somwehre start to go past f(x)

solve for x such that f(x)=g(x)
so
3x+30=x²+20
minus (3x+30) both sides
0=x²-3x-10
facotr
what 2 numbers multiply to get -10 and add to get -3?
-5 and 2
0=(x-5)(x+2)

set each to zero

0=x-5
5=x

0=x+2
-2=x

at x=5 and -2

test points between them
at x=-3, g(x)>f(x)
at x=0, f(x)>g(x)
at x=6, g(x)>f(x)


so g(x)>f(x) when x<-2 or x>5

so I think the teacher is looking for that point when g(x)<f(x) then g(x)>f(x)
so that would be at x=5