Answer:
The function [tex]f(x)=\frac{x-1}{3x+3}[/tex] is one-to-one function ⇒ 1st
The function [tex]f(x)=\sqrt{5x+9}[/tex] is one-to-one function ⇒ 2nd
The function [tex]f(x)=\frac{1}{2}x^{3}[/tex] is one-to-one function ⇒ 4th
Step-by-step explanation:
* Lets explain how to solve this problem
- One to one function is the function that has no reputation in the value
of the y-coordinates for every corresponding x-coordinates
- That means when you draw a horizontal line at any value of y, then
the horizontal line intersects the graph of the function at one point
only
- So to solve the problem look to the attached figures
# The red graph of the function [tex]f(x)=\frac{x-1}{3x+3}[/tex] ⇒1st graph
- In this graph if we draw a horizontal line at any value of y it will
intersect the graph at only one point
- Take care there is a horizontal asymptote at y= 1/3, that means
there is no value of x at y = 1/3
∴ The function [tex]f(x)=\frac{x-1}{3x+3}[/tex] is one-to-one function
# The blue graph of the function [tex]f(x)=\sqrt{5x+9}[/tex] ⇒2nd graph
- In this graph if we draw a horizontal line at any value of y it will
intersect the graph at only one point
∴ The function [tex]f(x)=\sqrt{5x+9}[/tex] is one-to-one function
# The green graph of the function [tex]f(x)=\frac{1}{2}x^{3}[/tex] ⇒3rd graph
- In this graph if we draw a horizontal line at any value of y it will
intersect the graph at only one point
∴ The function [tex]f(x)=\frac{1}{2}x^{3}[/tex] is one-to-one function
# The purple graph of the function [tex]f(x)=\frac{7}{4x^{2}}[/tex] ⇒5th graph
- In this graph if we draw a horizontal line at any value of y it will
intersect the graph at more than one point
∴ The function [tex]f(x)=\frac{7}{4x^{2}}[/tex] is not one-to-one function
# The black graph of the function [tex]f(x)=3x^{4}+7x^{3}[/tex] ⇒4th graph
- In this graph if we draw a horizontal line at any value of y it will
intersect the graph at more than one point
∴ The function [tex]f(x)=3x^{4}+7x^{3}[/tex] is not one-to-one function
* The answers are 1st , 2nd and 4th functions
