Let us add consecutive odd numbers and try to find any relationship.
1. 1
2. 1+3 = 4 ( square of 2 i.e 
)
3. 1+3+5 = 9 ( 
)
4. 1+3+5+7 = 16 (
)
5. 1+3+5+7+9 = 25 (
)
6. 1+3+5+7+9+11 = 36 ( 
)
7. 1+3+5+7+9+11+13 = 49 (
)
If we notice, the sum of the consecutive odd integers in each case is equal to the square of the place where it lies. For example, the sum of numbers in seventh place is equal to . The sum of the numbers in the fifth line is equal to .
Answer:
see below the first three problems
Step-by-step explanation:
f(g(-2))
First, find g(-2) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(-2) = -2(-2) + 1
g(-2) = 5
f(x) = 5x
f(5) = 5(5)
f(5) = 25
f(g(-2)) = 25
g(h(3))
First, find h(3) using function h(x). Then use that value as input for function g(x).
h(x) = x^2 + 6x + 8
h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8
h(3) = 35
g(x) = -2x + 1
g(35) = -2(35) + 1 = -70 + 1
g(35) = -69
g(h(3)) = -69
f(g(3a))
First, find g(3a) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(3a) = -2(3a) + 1
g(3a) = -6a + 1
f(x) = 5x
f(-6a + 1) = 5(-6a + 1)
f(-6a + 1) = -30a + 5
f(g(3a)) = -30a + 5
f(x) + g(x) = 5x - 3 - 2x + 7
= 3x + 4
Hope this helps! If you have any questions, feel free to ask.
