## leozap1 one year ago *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

1. anonymous

probs a good idea to multiply the functions

2. leozap1

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

3. anonymous

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

4. anonymous

now we need to find the domain.

5. anonymous

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

6. anonymous

with me?

7. leozap1

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

all g?

13. leozap1

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

14. leozap1

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

15. anonymous

$f/g=\frac{ x^2-16 }{ x+4 }$ $f/g=\frac{ (x-4)(x+4) }{ x+4 }$ $f/g=x-4$ 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 $f/g=x-4$ $\in R, \neq-4$

16. anonymous

17. leozap1

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

18. leozap1

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.

19. anonymous

looks good

20. leozap1

Thanks!