Question

Given f(x) = e^x and g(x) = x – 2, what is the range of (g*f)(x)

Answer 1

For this case we have the following functions:

$f (x) = e ^ x\\g (x) = x-2$

By definition we have to:

$(f * g) (x) = f (x) * g (x)$

Substituting:

$(f * g) (x) = e ^ x (x-2)$

The range of the function is given by all values of "and" valid. That is, all the real numbers.

ANswer:

(-∞,∞)

Graphic attached