hey, could someone help me with this question. Find the inverse of the function f(x)=3x-2
thank you
Hi,
When you find the inverse of a function you swap the \(x\) and \(y\) values of the function, ie. you want to make \(x=f\left(y\right)\).
For this problem
Rearrange \(x\) and \(y\) values of the function
1. \(x=3y-2\), now try and rearrange this by making \(y\) the subject
2. You should get \(y=\frac{x+2}{3}\) \(\therefore f^{-1}\left(x\right)=\frac{x+2}{3}\)
for functions, could someone explain placing restriction on inverse function on x values. thank you
I am not too sure what you mean by this, do you mind posting a particular example?
Please also remember that the condition for a function to be invertible or to have an inverse function is that it needs to be
one to one. Meaning that different \(x\) values map to different \(y\) values, to test if a function is one to one try using the horizontal line test.
For example, \(f\left(x\right)=x^2\) does not have an inverse function as it does not pass the horizontal line test, but \(f:[0,\infty )\to \mathbb{R},\:f\left(x\right)=x^2\) does have an inverse function, so does \(f:(-\infty ,0]\to \:\mathbb{R},\:f\left(x\right)=x^2\)
To help you understand this better I have made a desmos interactive graph, click
here to see!
hii, for this question f(x) =7x-4 would the inverse function be f -1(x) = x+4/7
thank you
Yes this is correct.
Hope this helps, and please do not spam the forums in an attempt to get an answer faster. Post as many methods questions you would like in this thread and somebody will help!