9514 1404 393
Answer:
B
Step-by-step explanation:
To find the inverse of y = f(x), solve the equation x = f(y) for y. For these functions, that's about the easiest way to do it.
A. x = ∛(3y) ⇒ x³ = 3y ⇒ x³/3 = y . . . . . does not match g(x)
B. x = 11y -4 ⇒ x +4 = 11y ⇒ (x +4)/11 = y . . . . matches g(x)
C. x = 3/y -10 ⇒ x +10 = 3/y ⇒ 3/(x+10) = y . . . . does not match g(x)
D. x = y/12 +15 ⇒ x -15 = y/12 ⇒ 12(x -15) = y . . . . does not match g(x)
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<em>Additional comment</em>
This is repeated application of the "solve for ..." process. In general, that process "undoes" what is "done" to the variable. The order of operations can tell you the order of the things that are done. The undoing is in the reverse order.
You need to be completely comfortable with the properties of equality (addition, subtraction, multiplication, division), and you need to understand the inverse functions of the functions we usually use: (powers, roots), (exponentials, logarithms), (trig functions, inverse trig functions). Of course, the inverse of addition is subtraction; the inverse of multiplication is division.
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Above, we used a "shortcut" a couple of times:
a = b/c ⇒ c = b/a . . . . . equivalent to multiplying both sides by c/a.
