In limits topic I came across a definition as |f|(x) = | f(x) |?

I know what the lateral means, but what is meant by the left hand size?

never seen it, but maybe it's akin to

(f◦g)(x) = f(g(x))

looks like you have some reading to do.

I can post a picture of the lecture note but this site doesn't allow this feature. It's hard to show it

In mathematics, the phrase "left-hand side" is used to refer to a particular side of an equation or an inequality. When working with equations or inequalities, it is common to have expressions on both sides of the equation or inequality symbol. The left-hand side (LHS) specifically refers to the expression on the left side, whereas the right-hand side (RHS) refers to the expression on the right side.

For example, in the equation x + 2 = 6, the left-hand side is x + 2, and the right-hand side is 6. The expression x + 2 is the one being manipulated or analyzed to solve the equation.

Now, let's apply this understanding to the definition you mentioned: |f|(x) = | f(x) |. Here, we have an equation that involves the absolute value of a function. The left-hand side, |f|(x), represents the absolute value of the function f at the input x. The right-hand side, | f(x) |, represents the absolute value of the value obtained by evaluating the function f at x.

To summarize, when encountering the phrase "left-hand side" in mathematics, it is important to distinguish it from the right-hand side. The left-hand side refers to the expression on the left side of an equation or inequality, while the right-hand side refers to the expression on the right side.