SOLUTION: Let f(x) = 3x – 42 and g(x) = 5x. Part 1 [4 points] What is (f ◦ g)(x) ? Part 2 [2 points] Use complete sentences to describe the method you used to solve this problem.

Algebra ->  Functions -> SOLUTION: Let f(x) = 3x – 42 and g(x) = 5x. Part 1 [4 points] What is (f ◦ g)(x) ? Part 2 [2 points] Use complete sentences to describe the method you used to solve this problem.      Log On


   

Question 341433: Let f(x) = 3x – 42 and g(x) = 5x.
Part 1 [4 points] What is (f ◦ g)(x) ?
Part 2 [2 points] Use complete sentences to describe the method you used to solve this problem.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 3x-42
g(x) = 5x

(fog)(x) is the same as f(g(x)).

This is interpreted as f of g of x.

You start with f(x) = 3x - 42

You replace x with g(x) to get:

f(g(x)) = 3*(g(x)) - 42

Since you know that g(x) = 5*x, you replace g(x) with 5*x in the equation to get:

f(5*x) = 3*(5*x) - 42

You simplify to get:

f(5*x) = 15*x - 42.

Since you know that 5*x = g(x), you can then simply state this equation as:

f(g(x)) = 15*x - 42.

What you are going is replacing x in f(x) with g(x) to get f(g(x)).

In functional notation, f(x) = 3*x - 42, f is the name of the function and x is the argument.

The argument is what the equation is working on.

if f(x) = 3*x - 42, then f(5) = 3*5 - 42 and f(z) = 3*z - 42.

The equation is the same.

The argument can change.

if f(x) = 3*x - 42, and you want to get f(74*y^3), then you would replace x with 74*y^3 to get:

f(74*y^3) = 3*(74*y^3) - 42.

All you do is replace the original argument with whatever you want it to be.

What we did was replace x with g(x) to get f(g(x)) = 3 * g(x) - 42.

Since we knew that g(x) was equal to 5*x, we then went in the equation and replaced g(x) with 5*x to get f(g(x)) = 3 * (5 * x) - 42.

We then simplified to get f(g(x)) = 15 * x - 42.