The inverse of f(x) = 3x³ + 8 is [tex]\sqrt[3]{\frac{x-8}{3}}[/tex].
Two functions f(x) and g(x) are inverse functions if (fog)x = x and (gof)x = x.
According to the given question we have to determine the inverse of f(x) = 3x³ + 8.
This can be written as
y = 3x³ + 8.
Now we'll switch x and y meaning everywhere there is x we'll replace with y and vice versa.
x = 3y³ + 8.
Now we'll solve for y.
3y³ = x - 8.
y³ = (x - 8)/3.
y = [tex]\sqrt[3]{\frac{x-8}{3}}[/tex].
f(x⁻¹) =[tex]\sqrt[3]{\frac{x-8}{3}}[/tex].
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