hello everyone welcome to senior pablo tv today we will be discussing inverse function okay first let us define the inverse function the inverse function is the relation formed when the independent variable is exchanged with the dependent variable in a given relation so let us explain we know that independent variable stands for our horizontal line horizontal line which is our x axis then the dependent variable is our vertical line which is our y axis then if we're going to interchange the two the horizontal or the x-axis to y-axis that will be the inverse function and put in mind that the inverse of a function may not always be a function so to better understand i'll kindly check our videos about relations and factorize now let's have this example find the inverse of 2 0 3 negative one four zero and five four so let's just interchange the value of x to the value of y so our answer is zero two just interchange negative one three zero four and four 5 okay take a look at our answer is it a function or not so we define a function if no x coordinate must be repeated so take a look we have two zeros it's our x so that means this is not attached so always put in mind our remember the inverse of a function will always be a function so that this is on how to uh find the inverse of our coordinates what if we have an equation let's say our example number one number one find the inverse of x minus four f of x is equal to x minus four so we have our four steps to find the inverse of a function if the given is an equation so i will write the four steps so that you will know all the step-by-step process number one replace f of x to y number two interchange x and y number three solve the new solve the new y from the equation in step two the equation in step number two and last number four replace the new y with f of negative replace the new y with f is negative one the inverse of x this is the inverse of x if the inverse is a function if the inverse is a function is a function okay so let us try to apply our steps in our example number one replace f of x to y so y replace y is equal to x minus four replace to y next interchange x and y so our y change to x x and our x change to y now step number three solve the new y from the equation in step two let us solve the y so it is transpose y so that will become negative y is equal to transpose x negative x then copy minus four transpose that will become negative y is equal to transpose negative x minus 4. now solve for y so to solve y let us eliminate the negative so multiply the equation by negative so this will become y because negative times negative u that is positive y is equal to negative times negative this will become positive x negative times we know that this is a function so replace the new y with inverse of x inverse of x is equal to x this is now our final answer the inverse of x minus 4 is x plus 4. okay listen how to solve the inverse of a function now i want you to try two x plus three raise this then by two x two x plus three okay this is two two x plus three if you want right please pause the video then if you're done answering resume watching pitch at your one so let us solve sir replace this will become y is equal to two f plus three and now interchange y it will become x and x will become y and copy now solve for y transpose negative 2y is equal to transpose negative x plus 3. now solve for y divide by negative two to eliminate our numerical coefficient negative two so y is equal to negative divided by negative that will become x then negative divided by negative minus 3 all over this is now our inversion function f of negative inverse of x is equal to x minus 3 over so this is now our final answer so that's it that is that is the inversive function just apply our four basic steps so if you are in the right path and solving then you can come up with the correct answer so that's the inverse of a function thank you for watching senior pablo tv stay tuned for the next videos [Applause]