Answer:
Part(B) is the correct answer
Step-by-step explanation:
Given functions are
f(x) = [tex]4x^3+5[/tex] and g(x) = [tex]\sqrt[3]{x-5/4}[/tex]
So both are inverse of each other
Since Definition of inverse function is
If a function f(x) is mapping from x to y , then the inverse function of f(x) maps
y back to x.
Solution
suppose
y = f(x)
y = [tex]4x^3+5[/tex]
in order to find inverse of f(x)
interchange the variables x and y
x = [tex]4y^3+5[/tex]
Now solve for y
Subtract 5 from both sides we get
[tex]4y^3[/tex] = x-5
Divide both sides by 4 we get
[tex]y^3[/tex] = (x-5)/4
[tex]y = \sqrt[3]{x-5/4}[/tex]
so this is the inverse of the f(x) and also from this we see that is [tex]g(x) = \sqrt[3]{x-5/4}[/tex]
This is Answer.
