Question

Which of the following functions I which of the following functions are one to one? Select all that apply there are 3 answers

Answer 1

Answer:

The function $f(x)=\frac{x-1}{3x+3}$ is one-to-one function ⇒ 1st

The function $f(x)=\sqrt{5x+9}$ is one-to-one function ⇒ 2nd

The function $f(x)=\frac{1}{2}x^{3}$ 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 $f(x)=\frac{x-1}{3x+3}$ ⇒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 $f(x)=\frac{x-1}{3x+3}$ is one-to-one function

# The blue graph of the function $f(x)=\sqrt{5x+9}$ ⇒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 $f(x)=\sqrt{5x+9}$ is one-to-one function

# The green graph of the function $f(x)=\frac{1}{2}x^{3}$ ⇒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 $f(x)=\frac{1}{2}x^{3}$ is one-to-one function

# The purple graph of the function $f(x)=\frac{7}{4x^{2}}$ ⇒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 $f(x)=\frac{7}{4x^{2}}$ is not one-to-one function

# The black graph of the function $f(x)=3x^{4}+7x^{3}$ ⇒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 $f(x)=3x^{4}+7x^{3}$ is not one-to-one function

* The answers are 1st , 2nd and 4th functions