Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 3 liters of
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Answer:
Remember, and the range of g must be in the domain of f.
a)
The domain of f(g(x)) and g(f(x)) is the set of reals.
b)
The domain of f(g(x)) is the set of nonnegative reals and the domain of g(f(x)) is the set of number such that
c)
The domain of f(g(x)) is the set of reals except the 1 and the domain of g(f(x)) is the set of reals except the 1 and -1
d)
The domain of f(g(x)) is the set of reals except 2, and the domain of g(f(x)) is the set of reals except -1.
e)
The domain of f(g(x)) is the set of nonnegative reals except -3. The domain of g(f(x)) is the set of nonnegative reals except -2.
Here's our equation:
Factor out the left side
(-2x - 3) - 4 = 3/4 (-8x - 12)
Simplify
-2x - 7 = 3/4 (-8x - 12)
Factor out the right side
-2x - 7 = -6x - 9
Add 7
-2x = 6x - 2
Add 6x to isolate the variable
4x = -2
Divide by 4
x = - 1/2
Here is how I simplified both sides initially. I'll only be showing the right side because this is a LOT of typing.
Begin with 3/4 (-8x - 12)
Use rule to multiply
3(-8x-12)/4
Factor 3(-8x-12)
(-8x - 12) = (-4 * 2x - 4 * 3)
Simplify (-4 * 2x - 4 * 3)
-3 * 4 (2x+3)
- 12 (2x + 3)
Now that we've factored 3/4 (-8x - 12), we're left with- 12 (2x + 3)/4.
12/4 =3, giving us -3(2x + 3)
Distribute and simplify, then you're done.