Answer:
option 3 ⇒ f⁻¹(x) = [tex]\frac{x^{2} -2 }{3} [/tex]
Step-by-step explanation:
Given F(x) = [tex]\sqrt{3x+2}[/tex]
let y = f(x)
y = [tex]\sqrt{3x+2}[/tex] ⇒ squaring the both sides
y² = 3x + 2 ⇒ subtract 2 from both sides
y² - 2 = 3x ⇒ divide both sides by 3
[tex]\frac{y^{2} -2 }{3} = x[/tex]
replace the location of x and y
∴ y = [tex]\frac{x^{2} -2 }{3} [/tex]
So, y will be f⁻¹(x)
∴ f⁻¹(x) = [tex]\frac{x^{2} -2 }{3} [/tex]
