Question

*Fan & medal* Please explain how I solve this. I have no idea how to do this, when I tried I ended up with -30x^2 - 6.
Let f(x) = -5x + 3 and g(x) = 6x - 2. Find f * g and its domain.
A.-30x^2 + 28x - 6; all real numbers except x = 1/3
B. -15x^2 - 8x - 12; all real numbers except x = 3/5
C. -30x^2 + 28x - 6; all real numbers
D. -15x^2 - 8x - 12; all real numbers

Answer 1

probs a good idea to multiply the functions

Answer 2

That's what I did, and I got -30x^2 - 6

Answer 3

\[f*g=(-5x+3)(6x-2)\]
\[f*g=-5x(6x-2)+3(6x-2)\]
\[f*g=-30x^2+10x+18x-6\]
\[f*g=-30x^2+28x-6\]

Answer 4

now we need to find the domain.

Answer 5

we can use to methods to find the domain; graphical method or algebra

Answer 6

with me?

Answer 7

Yea I see what I did wrong thank you. I don't know how to find the domain though.

Answer 8

well here there are only two functions with our proposed solution right; answers A and C

Answer 9

A says all real numbers except x=1/3 and C says x has solutions for all real numbers

Answer 10

so we say to our selves, if we plug x=1/3 into the equation, would we get a value for the function?

Answer 11

Sure we do. f(x)=0 for x=1/3. but thats still a solution of the function right? that number exists. hence our answer is C

Answer 12

all g?

Answer 13

Thanks! This really helps me. I also have some questions similar to this, but with division. Could you help me with it? Here is one of the questions. Let f(x) = x^2 - 16 and g(x) = x + 4. Find f/g and its domain. (1 point)
A. x + 4; all real numbers except x =/ 4
B. x + 4; all real numbers except x =/ -4
C. x - 4; all real numbers except x =/ 4
D. x - 4; all real numbers except x =/ -4

Answer 14

The =/ is suppose to be a does not equal to sign.

Answer 15

\[f/g=\frac{ x^2-16 }{ x+4 }\]
\[f/g=\frac{ (x-4)(x+4) }{ x+4 }\]
\[f/g=x-4\] and since the denominator of the previous step has x-4, then a function does not exist at a certain point when the denominator equals zero.
therefore
\[f/g=x-4\] \[\in R, \neq-4\]

Answer 16

hence answer is D

Answer 17

This one's a lot easier than the first, thank you.

Answer 18

Could you check my work on this last one? Let f(x) = -5x - 4 and g(x) = 6x - 7. Find f(x) + g(x). I got x-11 for this one.

Answer 19

looks good

Answer 20

Thanks!