Question

If f (x) = 2x2 – 5for - ♾ < x < 0,what is f-?(-2)?

Answer 1

To find the inverse, we:

• change f(x) to y

,

• interchange x and y

,

• solve for y

Thus,

`\begin{gathered} f(x)=2x^2-5 \\ y=2x^2-5 \\ x=2y^2-5 \\ 2y^2=x+5 \\ y^2=(x+5)/(2) \\ y=\pm\sqrt[]{(x+5)/(2)} \\ f^(-1)(x)=-\sqrt[]{(x+5)/(2)} \end{gathered}`

We take the "negative" part of the function since it is defined for - ♾ < x < 0.

We found inverse of f.

Now, to find f^(-1) (-2), we put -2 into the inverse and evaluate.

`\begin{gathered} f^(-1)(x)=-\sqrt[]{(x+5)/(2)} \\ f^(-1)(-2)=-\sqrt[]{(-2+5)/(2)} \\ =-\sqrt[]{(3)/(2)} \end{gathered}`