Respuesta :
Answer:
see explanation
Step-by-step explanation:
h(x) + k(x) = x² + 1 + x - 2 = x² + x - 1
(h + k)(2) = 2² + 2 - 1 = 4 + 2 - 1 = 5
h(x) - k(x) = x² + 1 - (x - 2) = x² + 1 - x + 2 = x² -x + 3
(h - k)(3) = 3² - 3 + 3 = 9 - 3 + 3 = 9
h(2) = 2² + 1 = 4 + 1 = 5
k(3) = 3 - 2 = 1
3h(2) + 2k(3) = (3 × 5) + (2 × 1) = 15 + 2 = 17
Answer:
(h + k)(2) = 5, (h – k)(3) =9 and 3h(2) + 2k(3) = 17.
Step-by-step explanation:
The given functions are
[tex]h(x)=x^2+1[/tex]
[tex]k(x)=x-2[/tex]
First find the values of functions at x=2 and x=3.
At x=2,
[tex]h(2)=(2)^2+1=5[/tex]
[tex]k(2)=2-2=0[/tex]
At x=3,
[tex]h(3)=(3)^2+1=10[/tex]
[tex]k(3)=3-2=1[/tex]
Now, use these values to find the required values.
[tex](h+k)(2)=h(2)+k(2)\rightarrow 5+0=5[/tex]
[tex](h-k)(3)=h(3)-k(3)\rightarrow 10-1=9[/tex]
[tex]3h(2)+2k(3)=3(5)+2(1)\rightarrow 15+2=17[/tex]
Therefore, (h + k)(2) = 5, (h – k)(3) =9 and 3h(2) + 2k(3) = 17.
