let f(x)=3x-3 and g(x)=2/x-1. evaluate:
a)2fg(2)
b){f/g-2f)(3)
c)(f-g)(4)
You have some matching problems with braces and parens, but
2(fg)(2) = 2*f(2)*g(2) = 2*3*2 = 12
(f/g-2f)(3) = f(3)/g(3) - 2f(3) = 6/1 - 2*6 = -6
(f-g)(4) = f(4)-g(4) = 9-2/3 = 8 1/3
kobe needs to step back and take a breath.
a. 2(3(2)-3) =6 b.(-6x^2+8)/(x-1) c.(12x^2-24x+4)/(x_1)
Answer
a) "2fg(2)" sounds like you're mixing math with gardening! But let's try to solve it anyway. First, let's evaluate g(2):
g(2) = 2/2-1
= 2/1
= 2
Now, we can substitute this value into f(x):
f(2) = 3(2) - 3
= 6 - 3
= 3
Finally, we multiply 3 by 2 to get:
2fg(2) = 2 * 3 * 2
= 12
So, 2fg(2) = 12. Voila!
b) Whoa, "{f/g-2f)(3)" seems like a math problem with a fancy hat! Let's break it down step by step. First, let's evaluate "f/g" at x = 3:
f(3) = 3(3) - 3
= 9 - 3
= 6
g(3) = 2/3 - 1
= 2/3 - 3/3
= -1/3
So, "f/g" at x = 3 is 6/(-1/3).
Now, let's evaluate "2f(3)":
2f(3) = 2(3(3) - 3)
= 2(9 - 3)
= 2(6)
= 12
Finally, let's subtract "2f(3)" from "{f/g" (yes, the fancy hat is back!):
{f/g-2f)(3) = (6/(-1/3)) - 12
= 6 * (-3) - 12
= -18 - 12
= -30
So, {f/g-2f)(3) = -30. That's the result!
c) "(f-g)(4)" - Looks like we have some subtraction within parentheses! Let's go for it. First, let's evaluate f(4) and g(4):
f(4) = 3(4) - 3
= 12 - 3
= 9
g(4) = 2/4 - 1
= 1/2 - 1
= -1/2
Now, let's subtract g(4) from f(4):
(f-g)(4) = f(4) - g(4)
= 9 - (-1/2)
= 9 + 1/2
= 18/2 + 1/2
= 19/2
So, (f-g)(4) = 19/2. There you have it!
To evaluate the given expressions, we need to apply the given functions to the provided values. Let's break down each expression one by one:
a) To evaluate 2fg(2), we first need to find g(2) and then multiply the result by 2f.
Start with g(x) = 2/(x-1). To find g(2), substitute x = 2:
g(2) = 2/(2-1)
= 2/1
= 2
Now, we can substitute this value into 2f:
2f = 2 * (3x-3)
= 2 * (3*2 - 3)
= 2 * (6 - 3)
= 2 * 3
= 6
Finally, multiply 2 and g(2):
2fg(2) = 2 * 6
= 12
Therefore, 2fg(2) evaluates to 12.
b) To evaluate {f/g-2f)(3), we first need to find f/g and then subtract 2f from the result.
Let's find f/g first. Start with f(x) = 3x-3 and g(x) = 2/(x-1):
f/g = (3x-3)/(2/(x-1))
To simplify this expression, we multiply the numerator by the reciprocal of the denominator (multiply by (x-1)/2):
f/g = (3x-3) * (x-1)/2
Next, substitute x = 3:
f/g = (3*3-3) * (3-1)/2
= 6 * 2/2
= 6
Now, subtract 2f from the result:
{f/g-2f)(3) = 6 - 2f(3)
= 6 - 2(3*3 - 3)
= 6 - 2(9 - 3)
= 6 - 2(6)
= 6 - 12
= -6
Therefore, {f/g-2f)(3) evaluates to -6.
c) To evaluate (f-g)(4), we need to subtract g(x) from f(x) and substitute x = 4:
f(x) = 3x - 3
g(x) = 2/(x-1)
(f-g)(4) = f(4) - g(4)
First, find f(4):
f(4) = 3(4) - 3
= 12 - 3
= 9
Next, find g(4):
g(4) = 2/(4-1)
= 2/3
Finally, subtract g(4) from f(4):
(f-g)(4) = f(4) - g(4)
= 9 - 2/3
Therefore, (f-g)(4) evaluates to 9 - 2/3.