Can you help me graph these inverse functions?

In summary, the conversation is about finding the inverse of three functions and graphing them for submission. The first function is y=x^2 where x is greater than or equal to 0. The second function is y=2log(base 10)x and the third is y=log(base 10)(x-1). It is suggested to look up standard math books for definitions of inverse functions and graphing can be done without calculating them.
  • #1
Ramandeep
6
0
Hey can you please help me with finding the inverse of these functions and a brief explanation for each:

y= x^2 (x> or equal to 0)

y= 2log(base 10) x

y= log (base 10) x-1

I need to submit each function and their inverse functions in one graph (three graphs for each function)

THANKSSSSS XXXXX
 
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  • #2
do you have any ides/thoughts on how to start?
 
  • #3
yeh I've done the first one, but i have no idea for the last two. please helppp x
 
  • #4
start with y(x) as given then rearrange for x in terms of y, x(y)

for the last two, you'll need to rasie everything to the power of e (or 10 depending on you definition of log)
 
Last edited:
  • #5
Ramandeep said:
Hey can you please help me with finding the inverse of these functions and a brief explanation for each:

y= x^2 (x> or equal to 0)

y= 2log(base 10) x

y= log (base 10) x-1

I need to submit each function and their inverse functions in one graph (three graphs for each function)

THANKSSSSS XXXXX

Did you keep your old schoolbooks? Or look up any standard fairly elementary (high school) math book. Square roots certainly and logarithms usually are defined as inverse functions in the first place!

Plus, since you have to graph, you can graph the inverse functions without even needing to calculate them!
 
  • #6
hey guys, I've completed these questions and done graphing thanks.
 

1. What is an inverse function?

An inverse function is a mathematical operation that reverses the effect of another function. In other words, if a function f(x) transforms a number x into another number y, its inverse function, denoted as f-1(y), will transform the number y back into x. This means that the input and output of the inverse function are switched compared to the original function.

2. How do you graph an inverse function?

To graph an inverse function, you can follow these steps:

  1. Find the inverse function by switching the x and y variables in the original function.
  2. Create a table of values for both the original and inverse function.
  3. Plot the points from the inverse function on a graph.
  4. Reflect the points over the line y=x to get the graph of the inverse function.

3. Is every function invertible?

No, not every function is invertible. For a function to have an inverse, it must pass the horizontal line test, meaning that every horizontal line intersects the graph of the function at most once. If a function fails this test, it is not one-to-one and therefore does not have an inverse function.

4. How can you tell if two functions are inverses of each other?

To determine if two functions are inverses of each other, you can use the composition test. This means that if you plug the function f(x) into the inverse function f-1(x) and simplify, you should get x. Similarly, if you plug the inverse function f-1(x) into the original function f(x) and simplify, you should also get x. If both of these conditions are met, then the functions are inverses of each other.

5. What is the relationship between the graphs of a function and its inverse?

The graphs of a function and its inverse are reflections of each other over the line y=x. This means that any point (x,y) on the graph of a function will have a corresponding point (y,x) on the graph of its inverse. Additionally, the domain and range of the function and its inverse are also switched. For example, if the original function has a domain of all real numbers except for 0, its inverse will have a range of all real numbers except for 0.

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