Answer:
The function whose inverse is also a function is:
[tex]f(x)=x^5-3[/tex]
Step-by-step explanation:
The inverse of a given function f(x) is also a function if the function is one and one.
a)
[tex]f(x)=\dfrac{|x+3|}{5}[/tex]
As we know that the modulus function is not one-one.
Hence, the inverse of this function is not a function.
b)
[tex]f(x)=x^5-3[/tex]
We know that a odd-degree polynomial is always one-one.
Hence, the inverse of this function is also a function.
c)
[tex]f(x)=\dfrac{x^4}{7}+27[/tex]
The even degree polynomial is not a one-one function.
Hence, it's inverse is not a function.
d)
[tex]f(x)=\dfrac{1}{x^2}[/tex]
We know that the graph of this function is not one-one and hence it's inverse is not a function.
