Afunction is given: f(x)=3x+12 a. determine the inverse of this function and name it g(x) b. use composite functions to show that these functions are inverses. c. f(g(– explain: what is the domain?

A. y = (x - 12)/3

B. See below

C. -2

Step-by-step explanation:

In general, to find the inverse of an equation like this, all you have to do is swap the x and y variables then solve for y.

First, replace "f(x)" with y... y = 3x + 12

Next, swap x and y... x = 3y + 12

Now, solve for y. You should get y = (x - 12)/3, and this is the inverse of f(x) = 3x + 12. Since the inverse is a different equation, you can rename "y" to be "g(x)" to help with part B.

Composite functions just mean you take one and plug it into the other. With inverses, plugging the functions into one another should return just x. In this case, you can take g(x) and plug it into f(x); so you can find f(g(x)).

Replace every instance of x with g(x). f(g(x) looks kind of weird, but it functions the same as every other function; you just plug something in and get something out.

f(g(x)) = 3[(x - 12)/3] + 12

Simplify; cancel out the 3s, add 12 and -12. What's left? x. This is how you know these two functions are inverses of one another. To help yourself visualize, plug them into a graphing calculator and see what inverses like compared to one another so you can understand how they behave graphically!

For part C, all you have to do is plug -2 into g(x) first, then plug the result of that into f(x). Try it on your own. g(-2) should give you -14/3, and when you plug that into f(x), you should end up with -2.

For the domain, you should recognize that both the inverse and the original function are linear. There are no square root symbols, logarithms, or variables in the denominators that would limit the domain (i.e. when you have x - 3 as the denominator, so you know you can't plug in 3 because it will give you 0 and you can't divide by zero). Since there's nothing to mess up the domain, it's all real numbers.

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column