Question

NEED HELP ASAP

if f(x)=sqrt x-3 and g(x)=1-x^2 then what did you notice about the domain of (f o g)(x)?

Answer 1

ANSWER

The domain is an empty set

EXPLANATION

The given functions are:

$f(x) = \sqrt{x - 3}$

and

$g(x) =1 - {x}^{2}$

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

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

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

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

This function is defined if and only if

$- {x}^{2} - 2 \geqslant 0$

${x}^{2} + 2 \leqslant 0$

There is no real values that satisfies this inequality, because

${x}^{2} + 2$

is always positive.

The domain of this composite function is a null set.

Answer 2

Answer:

The domain of f, and thus the range of g, is restricted to values greater than or equal to 3.

If 1 minus x squared is greater than or equal to 3, then x squared must be less than –2.

Since x squared cannot be less than a negative number, the function is undefined for all values of x.

Step-by-step explanation: