Question

Let f(x)=9-x^2, g(x)=3-x. Find (f-g)(x) and its domain

Answer 1

Answer:

$(f-g)(x)=-x^2+x+6$

Domain:

$(-\infty,\infty)$

Step-by-step explanation:

we are given

$f(x)=9-x^2$

$g(x)=3-x$

Calculation of (f-g)(x):

$(f-g)(x)=f(x)-g(x)$

we can plug it

$(f-g)(x)=9-x^2-(3-x)$

now, we can simplify it

$(f-g)(x)=9-x^2-3+x$

$(f-g)(x)=6-x^2+x$

$(f-g)(x)=-x^2+x+6$

Domain:

we know that

domain is all possible values of x for which any function is defined

and f(x),g(x) and (f-g)(x) are polynomials

so, domain will be all real numbers

so, we get

$(-\infty,\infty)$