Question

is the inverse of the function $f(x)=3x^2 - 2x + 1$ a function, and why or why not?
desmos | graphing calculator | north carolina version
a. yes, because $f(x)$ does not pass the horizontal line test.
b. no, because $f(x)$ does not pass the horizontal line test.
c. yes, because $f(x)$ passes the horizontal line test.
d. no, because $f(x)$ passes the horizontal line test.

Explanation:

Step1: Identify function type

The given function is $f(x)=3x^2-2x+1$, a quadratic (parabola).

Step2: Apply horizontal line test

A horizontal line will intersect a parabola (opening up/down) at 2 points. So $f(x)$ fails the test.

Step3: Relate to inverse function rule

A function has an inverse that is a function only if it passes the horizontal line test (one-to-one). Since $f(x)$ fails, its inverse is not a function.

Answer:

B. No, because f(x) does not pass the horizontal line test.