If the functions are inverses, then f(g(x)) = x.
A.

The functions are inverses of each other.
B. The domain of f(x) = x≠3. The domain of g(x) is x≠0.
The domain of f(g(x)) is (-∞, 0) ∪ (0, ∞).
The domain of g(f(x)) is (-∞, 3) ∪ (3, ∞).
Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2, 3)
m = = = 2, thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using B(2, 3), then
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = 2x - 1 ← equation of line
2x + 3y = 3
-10x + 2y = -32
Solve using the substitution method.
Solve for x in the first equation.
2x + 3y = 3
Subtract 3y from both sides.
2x = 3 - 3y
Divide both sides by 2.
x =
-
y
Plug x into the second equation.
-10(
-
y) + 2y = -32
Distribute -10 inside the parentheses.
-15 + 15y + 2y = -32
Combine like terms.
-15 + 17y = -32
Add 15 to both sides.
17y = -17
Divide both sides by 17.
y = -1
Plug y into the first equation.
2x + 3(-1) = 3
Multiply 3 by -1.
2x - 3 = 3
Add 3 to both sides.
2x = 6
Divide both sides by 2.
x = 3
x = 3;
y = -1
Maude - 225 albums, 135 heavy metal, 135/225 = 0.6 = probability of listening to heavy metal
Claude - 420 albums, 270 heavy metal, 270/420 = <span>0.64 (2 DP) = </span><span>probability of listening to heavy metal
Assuming the albums are picked randomly ... Claude has the highest probability of listening to heavy metal at 0.64 (2 DP), appose to Maude whose probability is less at 0.6.</span>