Question

Consider the function `f(x) = x^2- 5`. If `g(x) = f(x-7)`, what can be said of `g(x)`?

Answer 1

`g(x)=x^2-14x+44`

Explanation:

Confusion often arises in this kind of question because of the duplicate use of the place-holder variable `x`.
To avoid this, rewrite the original equation for `f(x)` substituting a different variable `s`
`color(white)("XXX")f(color(blue)(s))=color(blue)(s)^2-5`

Now if `g(x)=f(x-7)`

we can simply replace `color(blue)(s)` in our definition of `f(color(blue)(s))` with `color(red)(""(x-7))`

`color(white)("XXX")g(x)=f(color(red)((""x-7)))=color(red)(""(x-7))^2-5`

`color(white)("XXXXxX")=(x^2-14x+49)-5`

`color(white)("XXXxXX")=x^2-14x+44`