Answer:
Option (D) is true.
Step-by-step explanation:
Given the equation
25x⁴ - 625y - 500 = 0
solving in terms of y as a function of x
[tex]25x^4\:-\:625y\:-\:500\:=\:0[/tex]
Step 1: Add -25x⁴ to both sides
[tex]25x^4\:-\:625y\:-\:500\:+\:\left(-25x^4\right)=0+\left(-25x^4\right)[/tex]
[tex]-625y-500=-25x^4[/tex]
Step 2: Add 500 to both sides
[tex]-625y-500\:+500=-25x^4\:+500[/tex]
[tex]-625y=-25x^4\:+500[/tex]
Step 3: Divide both sides by -625
[tex]\frac{-625y}{-625}=\frac{\left(-25x^4\:+500\right)}{-625}[/tex]
[tex]\:\:y=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Therefore,
[tex]\:f\left(x\right)=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Thus, option (D) is true.
