f(x)=5x-6 and g(x)=8x^2 to evaluate each of the following A.(f+g)(6) B.(f-g)(-2) C.(fg)(5) D.(f/g)(0)

Question

f(x)=5x-6 and g(x)=8x^2 to evaluate each of the following A.(f+g)(6) B.(f-g)(-2) C.(fg)(5) D.(f/g)(0)

Answer 1

(f+g)x = f(x) + g(x)

5x-6 + 8x^2

If x =6, then

5(6) -6 + 8(6)^2

30-6+8(36)

24+288

312

 

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

(5x-6)-(8x^2)

If x=-2, then...

5(-2)-6 - 8(-2)^2

-10-6-32

-48

 

For multiplying and dividing, it's the same idea, except that it will be undefined for (f/g)(0).

Answer 2

A &B are adding & subtraction, so literally Combine Like Terms... (In done cases you will need to distribute the subtraction to all terms in g(x)--- but here g has only 1-term)

 

And since all terms are different, just rewrite in desending order (keeping +/- with the term itself...

A.

(f+g)= 5x-6 +8x²=   8x² + 5x - 6

 

B. (f-g) = 5x-6 -(8x²) =  -8x² + 5x - 6

 

 

C  multiply/ Distribute....  (fg) = (5x - 6 ) *8x²   or     

8x² * 5x  -   8x² *6      =>

8*5 x³     -  8*6 x²

40 x³      -   48 x^{2        (and that's it... yes you can skip steps above that you understand.)}

D make a fraction ÷

(f/g)   =  (5x-6) / (8x²)   so  x not = 0, since it would make denominator zero.

 

=    5x - 6      <--division bar)

       8x²