Answer: Option B
Step-by-step explanation:
By definition, only those functions that are one to one have an inverse function.
A function is one by one if there are not two different input values, [tex]x_1[/tex] and [tex]x_2[/tex], that have the same output value y
Note that the function [tex]f(x)= \frac{|x+3|}{5}[/tex] is not a one-to-one function
When x=2 [tex]f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1[/tex]
When x=8 [tex]f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1[/tex]
Note that the function [tex]f(x)= \frac{x^4}{7}+ 27[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
When x=-1 [tex]f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
Note that the function [tex]f(x)= \frac{1}{x^2}[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{1}{(1)^2}\ ,\ \ y=1[/tex]
When x=-1 [tex]f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1[/tex]
Then the answer is the option B.
You can verify that The function [tex]f (x) = x ^ 5-3[/tex] is a one-to-one function and therefore its inverse is a function
