Question

Can someone please explain this to me??
Let f(x) = -2x-7 and g(x) = -4x + 3. Find (f o g) (-5)

Answer 1

the (x) plug in -5 and you should then be able to answer the problem if i am thinking correct

Answer 2

When we deal a "composite function" notated "(f o g) (x)", we can read it like: "g(f(x))"
So that means we "put function f inside function g".
So, we know that:
\[f(x)= -2x-7\]
\[g(x)=-4x+3\]
So, we want to find the composite function of f on g, so we'll look at function g, and when we see an "x", we will place "-2x-7" on it's place.
Like this:
\[g(f(x))=-4(-2x-7)+3\]
Let's operate that:
\[g(f(x))=8x+28+3\]
\[g(f(x))=8x+31\]
and now, that we have the composite function, we can evaluate on the point we were asked to evaluate it in, wich is x=-5.
So let's take the function we just found and evaluate it:
\[g(f(x))=8x+31\]
then instead of "x" we'll put "-5":
\[g(f(-5))=8(-5)+31\]
doing some magical arithmetics:
\[g(f(-5))=-40+31\]
\[g(f(-5))=-9\]
And voilá, that concludes the exercise.
To resume what the steps are:
1) Find the "general" composite function, that means changing the "x" of one of the functions (careful with the order) and replace it with the function itself, confusing, I know, but you can always look at what I did above.

2) Evaluate the point in question, wich means, replacing the x's with the point.