Question

The point 3,4 lies on the graph of f(x)= sqrt(2x+a). Which ordered pair below lies on the graph of g(x)=1/2sqrt(2x+a)?

a)3/2,2
b)5/2,3/2
c)3,2
d)27,8

Answer 1

`(3;\ 4);\ f(x)=√(2x+a)\\\\√(2\cdot6+a)=4\\√(12+a)=4\ \ \ /^2\\12+a=16\\a=16-12\\a=4\\\\f(x)=√(2x+4)`


`g(x)=(1)/(2)√(2x+4)\\\\a)\ \left((3)/(2);\ 2\right)\\R=(1)/(2)\sqrt{2\cdot(3)/(2)+4}=(1)/(2)√(3+4)=(1)/(2)\sqrt7;\ L=2;\ L\\eq R\\\\b)\ \left((5)/(2);\ (3)/(2)\right)\\R=(1)/(2)\sqrt{2\cdot(5)/(2)+4}=(1)/(2)√(5+4)=(1)/(2)\sqrt9=(1)/(2)\cdot3=(3)/(2);\ L=(3)/(2);\ L=R`


`c)\ (3;\ 2)\\R=(1)/(2)√(2\cdot3+4)=(1)/(2)√(6+4)=(1)/(2)√(10);\ L=2;\ L\\eq R\\\\d)\ (27;\ 8)\\R=(1)/(2)√(2\cdot27+4)=(1)/(2)√(54+4)=(1)/(2)√(58);\ L=8;\ L\\eq R\\\\Answer:B`