Question

What is the range of `f(x) = -3^x + 4`?

Answer 1

Write `y=-3^x+4`

`=>3^x=4-y`

Take `ln` of both sides

`=>ln3^x=ln(4-y)`

`=>x=ln(4-y)/ln3`

Now notice that `(4-y)` cannot be negative nor zero!

`=>4-y>0 =>y<4`

Hence the range of `f(x)` is `f(x)<4`