Question

SOMEONE PLEASE HELP ME!!!
if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)

Answer 1

For this case, we have that by definition:

`(f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}`

We have the following functions:

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

So:

`(f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28`

On the other hand:

`(\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4`

`(\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3`

Answer:

`(f + g) (4) = 28\\(\frac {f} {g}(4)) = 3`

Answer 2

Replace x in each equation with 4:

f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21

g(x) = x^2-9 = 4^2 -9 = 16-9 =7

Now you have values for f(x) and g(x) now you can solve for f/g and f+g:

f/g = 21 / 7 = 3

f+g = 21 + 7 = 28