MaxWong

CPhill means you are correct

x= [0, 9].

#1 is correct.

#2 is wrong.

#2) g(f(-6))=g(-21)=-21 -2 = -23.

#3 is wrong.

#3) f(f(7))=f(31)=4(31) + 3 = 127 <- you forget to add that 3.

#4 is wrong but not completely wrong, you didn't simplify.

g(f(x)) = g(4x+3) = 4x+3 - 2 = 4x + 1.

1) We first have a list of what gives a remainder 2 when divided by 3 and we will have a list of what gives a remainder of 3 when divided by 7.

Gives a remainder 2 when divided by 3:

2,5,8,11,14,17,20,.......

Gives a remainder 3 when divided by 7:
3,10,17,......

Then we add 17 to the LCM of 3 and 7:

17 + 21 = 38

Answer : 38

Radius of the circle 'x^2+y^2=16'

= \(\sqrt{16}\)

= 4

\(\because 1<4\text{ and }2<4\)

\(\therefore \text{Point (1,2) is in the circle, and any line going through it can't be the circle's tangent}\)

\(\therefore \text{Any line going through the point (1,2) will ALWAYS intersect the circle }x^2+y^2=16\\ \;\;\;\;\text{at 2 points.}\)