to determine whether a function is one to one you can use the horizontal line test. when you use the horizontal line test, if there is more than one point on the horizontal line, then it is not one to one.
to find the inverse of a function, after graphing the function, you can switch the table of values so that what used to be x is now y and what used to be y is now x and what used to be the domain for the graph now becomes the range and what used to be the range becomes the domain. Basically you switch x and y.
whenever you have to solve an equation algebraically such as in an equation like (1.045)^t= 2,you would take the natural log or Ln of both sides and try to solve for t or x or any unknown. in this case after putting Ln on both sides,u would divide Ln 2 by Ln 1.045 and you would get what t equals.
whenever something has the base of e or the base of Ln, in order to get x or an unknown alone and u want to solve it, in the case of e, u would take the Ln of it and it would cancel and what ever you do to one side u would to to the other side and u would solve it. for example if its e^0.05t=3, u would Ln both sides lne^0.05t= Ln3 and after u solve it it would equal t = about 21.97 but if it had the base of Ln, then u would add the base of e to both sides and solve it
what i don't understand is when do we use log, is it only when something has the base of log or i don't know,. i also do not understand how to solve for two X's, such as in this equation 2^x + 2^-x =5. i also do not get how to prove f is its own inverse, such as in number 45 on page 44 and finding formulas for f-1 on page 44 numbers 43 and 44. i also don't really understand what solving an equation algebraically really mean, i just know what to do.
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to prove if f is the invers of f-1 you have to plug it in : (f o f-1)(x)
ReplyDeleteand it has to equal x in oder for it to be the inverse