f(x)=3x-7 and g(x) = -2x-6 find (fog)(4)
Well, "fog" sounds like an interesting combination of functions. It must be some kind of magical mist that makes math more entertaining! Let's see what happens when we let it loose on the number 4.
First, we need to find g(4). Plugging 4 into g(x) = -2x - 6, we get g(4) = -2(4) - 6 = -8 - 6 = -14.
Now, we can use the result of g(4) in f(x) = 3x - 7. Substituting -14 for x, we get f(-14) = 3(-14) - 7 = -42 - 7 = -49.
So, when we apply the magical mist of "fog" to the number 4, we get a final result of -49. Ta-da!
To find (f∘g)(4), we need to first find g(4) and then substitute that value into f(x). Let's start by finding g(4):
g(x) = -2x - 6
Now substitute x with 4:
g(4) = -2(4) - 6
g(4) = -8 - 6
g(4) = -14
Now that we know g(4) = -14, we can substitute this value into f(x):
f(x) = 3x - 7
Substitute x with -14:
fog(4) = f(g(4))
fog(4) = f(-14)
fog(4) = 3(-14) - 7
fog(4) = -42 - 7
fog(4) = -49
Therefore, (f∘g)(4) = -49.
To find (f ◦ g)(4), we need to first evaluate g(4) and then substitute that result into f(x).
Given the function g(x) = -2x - 6, we substitute x = 4 to find g(4):
g(4) = -2(4) - 6 = -8 - 6 = -14.
Now that we have g(4) = -14, we substitute it into f(x) = 3x - 7:
(f ◦ g)(4) = f(g(4)) = f(-14).
Substituting -14 into f(x), we get:
f(-14) = 3(-14) - 7 = -42 - 7 = -49.
Therefore, (f ◦ g)(4) = -49.
(fog)(4) = f( g(4) ) , g(4) = -2(4)-6 = -14
= f(-14)
= 3(-14) - 7
= -49
or
f( g(x) )
= f(-2x-6)
= 3(-2x-6) - 7
= -6x - 25
f( g(4) ) = -6(4) - 25 = -49