Determine whether the following statement makes sense or does not make sense, and explain your reasoning (modified from true/false format of text):
If f(x) = 3x, then f^-1(x) = 1/3x
A) This makes sense because the inverse would divide by 3 to "undo" the multiplication by 3 in f(x).
B) This does not make sense because although we would divide by 3 to "undo" the multiplication by 3 in f(x), the x would appear in the numerator not the denominator.
The correct answer is B) This does not make sense because although we would divide by 3 to "undo" the multiplication by 3 in f(x), the x would appear in the numerator, not the denominator.
To determine whether this statement makes sense or not, we need to understand the concept of function inverses. The inverse of a function f(x) undoes the operation of the original function, such that applying f and its inverse, denoted as f^-1, in sequence will give the original input x.
In this case, the original function f(x) = 3x multiplies the input x by 3. To find the inverse function f^-1(x), we need to undo this multiplication by dividing by 3. So the correct way to write the inverse function would be: f^-1(x) = x/3, rather than 1/3x.
Therefore, option B is the correct answer. The given statement does not make sense because the x would appear in the numerator, not the denominator, when expressing the inverse of the function f(x) = 3x.