Question

How do you find g(5n) given `g(x)=x^2-x`?

Answer 1

`g(5n) = 25n^2 - 5n`

Explanation:

Simply replace the `x` in the function's formula with whatever you see in the parentheses to evaluate `g` at that point. We get:

`g(5n) = (5n)^2 - 5n`

Recall that `(ab)^2 = a^2b^2`, so:

`g(5n) = 25 * n^2 - 5n`

The tricky part here is that parentheses like `(5n)^2` are often omitted (which is obviously a mistake) and are often interpreted like `5n^2`, which just means `5` times `n^2`, or `25n`, which means `5^2 * n` (again, those are just common mistakes). However, the correct way is to always use them when substituting a "bigger" term in place of a smaller one, for example when using `abc` instead of `d` in the formula `d^3`, the correct substitution is `(abc)^3 = a^3b^3c^3`, and none other.