Question

Plz Help

Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5.

1.k(x)=40-3^x+1-15x
2.k(x)=3^x-3x k(x)
3.k(x)=10+3^x+1-15x k(x)
4.k(x)=10-3^x-3x k(x)
5.k(x)=40-5(3^x)-9x k(x)
6.k(x)=5(3^x)-9x-10 k(x)
1. k(x) = (5g + 3h)(x)
2. k(x) = (3h - 5g)(x)
3. k(x) = (3g + 5h)(x)
4. k(x) = (5h - 3g)(x)
5. k(x) = (h - g)(x)
6. k(x) = (g + h)(x)

Answer 1

1 - 3, 2 - 5, 3 - 4, 4 - 6, 5 - 1, 6 - 2.

Explanation:

We have,

h(x) = 5-3x and
`g(x) = -3^x+5`

So, according to the options, we have,

1. k(x) = (5g + 3h)(x)

Now,
`k(x)=(5g+3h)(x)=5g(x)+3h(x)`

i.e.
`k(x)=5(-3^x+5)+3(5-3x)`

i.e.
`k(x)=5(-3^x)+25+15-9x`

i.e.
`k(x)=40-5(3^x)-9x`

2. k(x) = (3h - 5g)(x)

Now,
`k(x)=(3h-5g)(x)=3h(x)-5g(x)`

i.e.
`k(x)=3(5-3x)-5(-3^x+5)`

i.e.
`k(x)=15-9x-5(-3^x)-25`

i.e.
`k(x)=-9x+5(3^x)-10`

3. k(x) = (3g + 5h)(x)

Now,
`k(x)=(3g+5h)(x)=3g(x)+5h(x)`

i.e.
`k(x)=3(-3^x+5)+5(5-3x)`

i.e.
`k(x)=3(-3^x)+15+25-15x`

i.e.
`k(x)=-3^(x+1)+40-15x`

4. k(x) = (5h - 3g)(x)

Now,
`k(x)=(3h-5g)(x)=3h(x)-5g(x)`

i.e.
`k(x)=5(5-3x)-3(-3^x+5)`

i.e.
`k(x)=25-15x-3(3^x)-15`

i.e.
`k(x)=-15x-3^(x+1)+10`

5. k(x) = (h - g)(x)

Now,
`k(x)=(h-g)(x)=h(x)-g(x)`

i.e.
`k(x)=(5-3x)-(-3^x+5)`

i.e.
`k(x)=5-3x+3^x-5`

i.e.
`k(x)=-3x+3^x`

6. k(x) = (g + h)(x)

Now,
`k(x)=(g+h)(x)=g(x)+h(x)`

i.e.
`k(x)=(-3^x+5)+(5-3x)`

i.e.
`k(x)=-3^x+10-3x`

Thus, we have the matches as,

1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x

6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x