Determine whether the function is one-to-one.
-$$f ( x ) = 7 x ^ { 2 } - 6$$

Question

Quizplus · Accepted Answer

To show that a function is not one-to-one, we need to find two distinct inputs that produce the same output. Let's solve for $f(x)$ and set it equal to some constant, say $c$:

\begin{align*}
7x^2 - 6 &= c \
7x^2 &= c + 6 \
x^2 &= \frac{c+6}{7} \
x &= \pm \sqrt{\frac{c+6}{7}}
\end{align*}

Notice that the equation above gives us two possible values of $x$ for each value of $c$ (except for $c=-6$, which is not in the range of $f(x)$). Therefore, we have found distinct inputs that produce the same output, which means that $f(x)$ is not one-to-one.

Determine Whether the Function Is One-To-One f(x)=7x2−6f ( x ) = 7 x ^ { 2 } - 6f(x)=7x2−6

Determine Whether the Function Is One-To-One $f ( x ) = 7 x ^ { 2 } - 6$