Question

If f(x) = 2x + 3 and g(x) = x2 − 1, find the values of combining these functions. Match each combined function to its corresponding value. Tiles (f + g)(2) (f − g)(4) (f ÷ g)(2) (f × g)(1) Pairs -4 arrowBoth arrowBoth 10 arrowBoth 0 arrowBoth

Answer 1

We determine the answers to these items by substituting the values before performing the operation.
1) (f + g)(2) f(2) = 2(2) + 3 = 7 g(2) = 2² - 1 = 3 (f + g)(2) = 7 + 3 = 10 (Answer for 1 is B)
2) (f - g)(4) f(4) = 2(4) + 3 = 11 g(4) = 4² - 1 = 15 (f - g)(4) = 11 - 15 = -4 (Answer for 2 is A)
3) (f ÷ g)(2) (f x g)(1)
We already have the values of f(2) and g(2) above (in number 1) f(1) = 2(1) + 3 = 5 g(1) = 1² - 1 = 0

The answer to this item is zero because any number multiplied to zero is zero. Letter C.

Answer 2

`(f+g)(2)=10`

`(f-g)(4)=-4`

(f÷ g)(2)=
`(7)/(3)`

`(f*g)(1)=0`

Explanation:

`f(x) = 2x + 3` and
`g(x) = x^2 - 1`

Lets find f(2) , f(4) , g(4) and g(2)

`f(x) = 2x + 3[/tex</p><p>[tex]f(2) = 2(2) + 3=7`

`f(4) = 2(4) + 3=11`

`f(1) = 2(1) + 3=5`

`g(x) = x^2 - 1`

`g(2) = 2^2 - 1=3`

`g(4) = 4^2 - 1=15`

`g(1) = 1^2 - 1=0`

LEts find (f+g)(2)

`(f+g)(2)= f(2) + g(2)=7+3=10`

`(f-g)(4)= f(4) - g(4)=11-15=-4`

(f÷ g)(2)=
`(f(2))/(g(2)) =(7)/(3)`

`(f*g)(1)= f(1) * g(1)=5*0=0`