Question

Let f (x) = 1/x and g(x) = x² – 3x. What two numbers are not in the domain of fºg?

Answer 1

For this case we have the following equations:

$f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x$

We must find $(f_ {o} g) (x):$

By definition of composition of functions we have to:

$(f_ {o} g) (x) = f (g (x))$

So:

$(f_ {o} g) (x) = \frac {1} {x ^ 2-3x}$

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

$x ^ 2-3x = 0\\x (x-3) = 0$

So, the roots are:

$x_ {1} = 0\\x_ {2} = 3$

The domain is given by all real numbers except 0 and 3.

Answer:

x other than 0 and 3

Answer 2

ANSWER

0 and 3

EXPLANATION

The given functions are

$f(x) = \frac{1}{x}$

and

$g(x) = {x}^{2} - 3x$

$( f \circ g)(x) = f(g(x))$

$( f \circ g)(x) = f( {x}^{2} -x )$

$( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x}$

Factor the numerator:

$( f \circ g)(x) = \frac{1}{ x(x - 3)}$

The function will be undefined if the denominator is zero.

$x(x - 3) \ne0$

$x \ne0 \: and \: x \ne3$

Therefore 0 and not in the domain of the composed function.