So this week we went over domain & range and inverse functions. I'm still kinda iffy on the domain & range portion of everything but I'm going to see if my sister can help me with that quickly before tomorrow's test. Anyhow, inverse functions are pretty simple. Probably the simplest thing I will learn in this class.
- First you switch x and y then you solve for y but before you do this, you have to try out the horizontal line test. When graphing the equation, if the x axis is touches more than once, it does not have an inverse.
- After you find an inverse, you have to prove it actually is an inverse. Do this by plugging the inverse into the original equation and vise versa.
f(x) f^-1(x)
- If both problems come out equalling x, you did it correctly and that is indeed an inverse.
Eg: y=5x-2
- Graph it and see that it only touches the x axis once.
- Switch the x and y:
x=5y-2
Solve for y:
x-2=5y
x+2/5=y - Prove:
y=5(x+2/5)-2
=x+2-2
=x
y=(5x-2)/5+2
=x-2+2
=x
For domain and range, you have to remember what u need to do for each problem. Everything has a domain but you can only find range for polynomials and absolute values.
ReplyDeleteFor domains:
-Polynomials and absolute values will always be (-infinity, infinity). Thats quite simple.
-For fractions, set the bottom =0 and solve for x.
Lets say x= +/-5. Your answer would look like: (-infinity,-5)U(-5,5)U(5,infinity).
-For square roots, solve for x. Then put ur answer on a number line and plug in a number on each side of that number as f(x). If ur number is negative, it doesn't work but if positive, it will work. Then set ur answer as either [-#,infinity) or (-infinity,#].
For range:
-For polynomials, to find range, find x=-b/2a and put a bracket next to ur number (not infinity).
-For absolute values, the range will be the number outside the absolute value.
Ex: /x+4/-1...ur range will be [-1,infinity).
One thing i forgot to mention for range of polynomials. If it is odd then the range will be (-infinity,infinity).
ReplyDeleteThe x=-b/2a is for whenever there is a quadratic and that gives u the vertex.