This concept is new to me. I am doing a university level class and the way this class is presented is very theoretical that I even struggle to read the symbols (except in a very slow way). Because of this concepts that I thought I previously understood and how they interrelate, I suddenly feel like I don't understand, and am getting them confused (e.g., one to one, increasing/decreasing, monotonicity, etc etc).
The question I am struggling with is:
Consider the function, $f(x) = x^3 -4$ and take its reflection in the line $y = x$.
Because $f(x)$ is monotone we know that its reflection describes the graph of another function $g(x)$.
What is its formula?
So I have managed (I think) to take the reflection in the line $y = x$:
$f(x) = x^{\frac13} – 4$, but I am really unsure how to proceed from here.
Could someone help me understand this and how it is related to increasing across the domain?
Best Answer
given:
$f(x)=x^3-4$ or $y=x^3-4$
for reflection of any function $f(x)$ about the line $y=x$, exchange $x$ & $y$ or put $y=x$ and $x=y$ in given function $f(x)$
$$x=y^3-4$$
$$y^3=x+4$$
$$y=(x+4)^{1/3}$$ above function is reflection of $f(x) $ about line y=x