Question

For the following pairs of functions, state the domain of (f*g)(x).
Question(s) can be found at the bottom or in the following image.
http://prntscr.com/2gxntf

Answer 1

\[a) f(x)=\frac{ 1 }{ x^2-5x-14 } and g(x)=\sec x\]

Answer 2

make sure that
\[x^2-5x-14\neq 0\] and also that \(\cos(x)\neq 0\)

Answer 3

first one is easy enough because
\[x^2-5x-14=(x-7)(x+2)\] so the zeros are easy to find

Answer 4

Multiplying them you get :
\[\huge \frac{ \sec x }{ x^2 -5x - 14 }\]
just set the denominator to equal zero , what ever the roots are is you would put
the domain is all real numbers except (the roots of that equation)

Answer 5

and since \(\sec(x)=\frac{1}{\cos(x)}\) you also have to make sure that \(\cos(x)\neq 0\)

Answer 6

The domain for a rational function is all real numbers except that would make the denominator equal zero ( dividing by zero is undefined).

Answer 7

I only got XER, x cannot equal 7 or -2, but the answer also includes that x can't be pi/2 or 3pi/2

Answer 8

Ohh, okay. Thanks, I get it now. Also, I'm not quite sure how to approach these.

\[b) f(x)=99^x ;g(x)=\log(x-8)\]
\[c) f(x)=\sqrt{x+81};g(x)=\csc(x)\]
\[d) f(x)=\log(x^2+6c+9);g(c)=\sqrt{x^2-1}\]

Answer 9

domain {x | x≠2,-7, pi/2 + k(pi), where k is an integer}

Answer 10

I'm not sure how to approach questions b-d though