Question

Which of the following equations represents y as a function of x? (A) 3y^4 + 2x – 7 = 1 (B) x^2 y + x = 4y (C) Both (A) and (B) (D) Neither (A) nor (B)

Answer 1

(C) Both (A) and (B)

Step-by-step explanation

Step 1

a function where y is a function of x is given by:

`y=f(x)`

isolating y in (A)

`\begin{gathered} 3y^4+2x-7=1 \\ 3y^4=1-2x+7 \\ 3y^4=-2x+8 \\ y^4=(-2x+8)/(3) \\ y=\pm\sqrt[4]{-2x+8} \\ \\ \end{gathered}`

then, A is a function

Step 2

isolating y in (B)

`\begin{gathered} x^2y+x=4y \\ +x=4y-x^2y \\ x=y(4-x^2) \\ y=(x)/(4-x^2) \end{gathered}`

then, (B) is an equation that represents y as a function on x

I hope this helps you.