Question

If m(x) = x+5/x-1 and n(x) = x — 3, have the same domain as (m • n) (x)

Answer 1

For this case we have the following functions:

$m (x) = \frac {x + 5} {x-1}\\n (x) = x-3$

By definition we have to:

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

So:

$(m * n) (x) = m (x) * n (x)\\(m * n) (x) = \frac {x + 5} {x-1} (x-3)\\(m * n) (x) = \frac {(x + 5) (x-3)} {x-1}$

By definition, the domain of a function is given by the values for which the function is defined.

The domain of m(x) is given by all reals except 1.

The domain of n(x) is given by all reals.

While the domain of $(m * n) (x)$ is given by:

All reals, except the 1. With $x = 1$, the denominator is 0 and the function is no longer defined.

Answer:

Domain of$(m * n) (x)$ is given by all reals except 1.