I'm stuck on a few problems that I have absolutely no idea how to do.
1) Inverse of the function. f(x)=2 + \sqrt(x-5)
2) f(x)=3x^2 - 6x + 9. Find f(x+h)
1) Inverse of the function. f(x)=2 + \sqrt(x-5)
2) f(x)=3x^2 - 6x + 9. Find f(x+h)
-
in some programming languages, "\" means integer division, but I don't know what it is supposed to mean in your first problem. I'll just ignore it and assume the function is f(x)=2 + sqrt(x-5)
an inverse function simply undoes what some other function does, so that you get your original number (argument of the function) back.
simple example: f(x) = x+1
this function takes a number, x, and adds 1 to it. how would you undo that? simply subtract 1. addition and subtraction are inverse operations, just as multiplication and division are.
if you undo all the operations (basically solving for x), you get:
5+[f(x)-2]^2 = x
writing it as a new function, we replace the f(x) with our argument variable, and replace the x on the right with a function name. putting a superscript "-1" on the f indicates that it is an inverse function.
f^-1(x) = x^2 + 5
for second problem, you're asked to evaluate the function when the argument is x+h.
if you were going to evaluate it when x=5, you would replace every x with 5 and perform the indicated operations. well, you do the same thing, but instead of 5, use x+h
f(x)=3x^2 - 6x + 9
f(x+h)=3(x+h)^2 - 6(x+h) + 9
you can then expand and simplify the right hand side to obtain the final answer.
an inverse function simply undoes what some other function does, so that you get your original number (argument of the function) back.
simple example: f(x) = x+1
this function takes a number, x, and adds 1 to it. how would you undo that? simply subtract 1. addition and subtraction are inverse operations, just as multiplication and division are.
if you undo all the operations (basically solving for x), you get:
5+[f(x)-2]^2 = x
writing it as a new function, we replace the f(x) with our argument variable, and replace the x on the right with a function name. putting a superscript "-1" on the f indicates that it is an inverse function.
f^-1(x) = x^2 + 5
for second problem, you're asked to evaluate the function when the argument is x+h.
if you were going to evaluate it when x=5, you would replace every x with 5 and perform the indicated operations. well, you do the same thing, but instead of 5, use x+h
f(x)=3x^2 - 6x + 9
f(x+h)=3(x+h)^2 - 6(x+h) + 9
you can then expand and simplify the right hand side to obtain the final answer.
-
1) (x-2)squared -5=inverse
to find the inverse just switch the x and y, then solve for y (aka your inverse)
2) 3(x+h)squared-6(x+h)+9
unless there is more info you didn't give this is all i know. take what ever is in the (X), in this case (x+h) and plug it in the equation where ever you see an "x"
to find the inverse just switch the x and y, then solve for y (aka your inverse)
2) 3(x+h)squared-6(x+h)+9
unless there is more info you didn't give this is all i know. take what ever is in the (X), in this case (x+h) and plug it in the equation where ever you see an "x"
-
Inverse function = 1 / f(x)
f(x+h)= 3(x+h)^2
Just expand.
f(x+h)= 3(x+h)^2
Just expand.
-
THATS NOT COLLEGE ALGEBRA:) I HAD THAT KIND OF MATH WHEN I WAS IN 2ND GRADE:P