The product of two numbers is 12. the sum of the larger number and twice the smaller is 11. find the two numbers

Step-by-step explanation:

let x>y

x+2y=11

x=11-2y

xy=12

(11-2y)y=12

11 y-2 y^2=12

2 y^2-11 y+12=0

2y²-8y-3y+12=0

2y(y-4)-3(y-4)=0

(y-4)(2y-3)=0

y=4,3/2

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7