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.

You have to be careful with the term inverse funtion.That is not the same as reciprocal.

if f(x)=3x=y
then the inverse can be found this way:
y=3x
x=3y
y=x/3 or f^-1(x)=x/3

check: inverse(function)must equal x

so f^-1 (f)= 3(x/3)=x so in fact it is the inverse.
So false. Go with B. When dealing with functions, the term "inverse" seldom means reciprocal.

Please help HM

are u sure about this

Christian -- Bobpursley is a math/physics/teacher. HM is probably a high school student.

Yes, Christian. But don't trust me. http://www.youtube.com/watch?v=Ec5YYVxyq44 That is the same message.

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 the statement makes sense, we need to understand the concept of the inverse function. Given a function f(x), the inverse function, denoted as f^(-1)(x), "undoes" the original function f(x) by reversing the input and output.

In this case, the function f(x) = 3x is a simple linear function that multiplies the input x by 3. To find the inverse function f^(-1)(x), we need to "undo" this multiplication.

To find the inverse of f(x), we start by replacing f(x) with y:
y = 3x

Next, we swap x and y:
x = 3y

Now, we solve this equation for y to find the inverse function:
x = 3y
x/3 = y

Therefore, the inverse function f^(-1)(x) = x/3.

So, the correct statement would be: "If f(x) = 3x, then f^(-1)(x) = x/3."