form the things that i leared this week about logs is that the it is an exponential function. Logs are a way to find out what exponent equals to the answer. Log is always base ten unless it has a base. When there is an equation for example : log2(9)=3 the base always goes under and to the other side : 9=3^2.
Another thing that we leared this is ln(natural log). Ln is just like log but it is base e. e is just like pie it equals a number.
you are able to use log and ln to use to solve equations and to figure out exponential functions.
This week we also leared about inverses and how to find then. the inverse of f(x) is f^-1(x)
to find the inverse you need to verify that: (f o f^-1)=x & (f^-1 o f )=x.
If it does not equal x then it is not an inverse.
for example: x^2 is the inverse of square root of x
questions: the only question that i have is the on how to find the inverse by solving it.
To find the inverse by solving it you just switch the x and y placement for instance if
ReplyDeletef(x)=2x+3 you switch the x and y and you get
x=2y+3 subtract 3 to both sides
x-3=2y now divide 2 to both sides
x-3=y so the answer is
2
f^-1(x)= x-3
2
and in order to graph it without figuring out the equation just switch the input and output points
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ReplyDeleteto find the inverse by solving it
ReplyDeletefirst you switch x with y like this
y=5x-3 to find the inverse it becomes
x=5y-3 then you solve for x
x+3=5y
x+3 / 5= y
solving for the inverse is easy i'll help you with more detail if you dont understand.
ReplyDeleteyou basically switch the inout and make it your output.
ex.
y=3x+6
you switch the x with the y.
so, it would be like your solving for x.
x=3y+6
x-6=3y, divide by 3
x-6/3=y
x-2=y (:
hope i helped. (: