Question

Suppose y=3t+5 and x=21t^2. Write a function of f(x) that determines y in terms of x. (Assume that t≥0)

Answer 1

`y=\sqrt{(3)/(7)x}+5`

Explanation:

Suppose
`y=3t+5` and
`x=21t^2.`

Express t from the first equation:

`3t=y-5\\ \\t=(y-5)/(3)`

Substitute it into the second equation:

`x=21\left((y-5)/(3)\right)^2\\ \\x=21\cdot((y-5)^2)/(9)\\ \\(y-5)^2=(9)/(21)x\\ \\y-5=\pm \sqrt{(3)/(7)x}`

Since
`t\ge 0,` then
`y-5\ge 0,` so

`y-5=\sqrt{(3)/(7)x}\\ \\y=\sqrt{(3)/(7)x}+5`