I have the following piecewise function $ f(x) $:
And I have to find the $\lim_{x \to -1^{-}} f(x^2) $
I have defined approximately the piecewise function $ f(x) $ based on the graph:
\begin{align} f(x) = \begin{cases} \approx\frac{3}{2}x + \frac{7}{2} &, -\infty < x < -1 \\ \approx3 &, x = -1 \\ 2 &, -1 < x < 1 \\ \approx3 &, x = 1 \\ 1& , 1 < x < \infty \\ \end{cases} \end{align}
If I were looking for the limit for $\lim_{x \to -1^{-}} f(x) $ the answer would be $ 2 $ but I'm confused when it comes to $ f(x^2) $.
The answer provided is $ 1 $ but I can't figure out how the function is transformed when is squared so the limit approaches 1.
Using the sequential definition of the limit or otherwise one has $$\lim_{x\to-1^-}f(x^2)=\lim_{y\to1^+}f(y)=1$$