Question

Given g(x)=3x+6, find the value of x when g(x)=30.

Answer 1

Answer: 15x-30

Step-by-step explanation:

This is a composite function, which means you are combining two functions together. This can seem tricky, but once you understand how to break these problems into pieces it becomes much easier.

 

g(f(x)) can be read as g of f of x. Which means we are plugging the function f(x) into the function g(x). Think of it like this, if I were to ask you to find g(3) you would need to plug the value 3 into the function g(x). This would look like this: g(3) = 5(3)              So g(3)= 15

     However, when we are working with a composite function instead of a whole number we want to first look at the second function, so that we can rewrite the problem. In this problem f(x) = 3x -6

                               So, I can rewrite this as g(3x -6)

• Now, all you have to do is plug this function into g (x) just like I plugged in the value of 3 above. This will look like this:

                               g(3x-6) = 5(3x-6)

•  Then, you just need to multiply each term by 5, following the distributive property:

                                g(3x-6) = 15x - 30