Question

Find the inverse of the function. Is the inverse a function?y=5x^2-3

Answer 1

Answer:

C.

$y=\pm\sqrt[]{\frac{x+3}{5}}$

No, it is not a function

Step-by-step Explanation:

Given the below equation;

$y=5x^2-3$

We'll follow the below steps to find its inverse;

Step 1: Switch the positions of x and y;

$x=5y^2-3$

Step 2: Solve for y by first adding 3 to both sides of the equation;

$\begin{gathered} x+3=5y^2-3+3 \\ x+3=5y^2 \end{gathered}$

Step 3: Divide both sides by 5;

$\begin{gathered} \frac{x+3}{5}=\frac{5y^2}{5} \\ \frac{x+3}{5}=y^2 \end{gathered}$

Step 4: Take the square root of both sides;

$y=\pm\sqrt[]{\frac{x+3}{5}}$

The above is the inverse of the given function.

Note that in a function, each input is associated with exactly one output. Looking at the inverse of the function, we can see that some x values will yield two values of y, a negative and a positive value, therefore we can say that it is not a function since an input can produce more than one output value.

So the inverse of the function is not a function.