Solving an Equation for an Unknown Function Suppose that g ( x ) = 2 x + 1 h ( x ) = 4 x 2 + 4 x + 7 Find a function f such that f ∘ g = h . (Think about what operation you would have to perform on the formula for g to end up with the formula for h.) Now suppose that f ( x ) = 3 x + 5 h ( x ) = 3 x 2 + 3 x + 2 Use the same sort of reasoning to find a function g such that f ∘ g = h
Solving an Equation for an Unknown Function Suppose that g ( x ) = 2 x + 1 h ( x ) = 4 x 2 + 4 x + 7 Find a function f such that f ∘ g = h . (Think about what operation you would have to perform on the formula for g to end up with the formula for h.) Now suppose that f ( x ) = 3 x + 5 h ( x ) = 3 x 2 + 3 x + 2 Use the same sort of reasoning to find a function g such that f ∘ g = h
Solution Summary: The author explains that the functions to obtain f are, cg(x)=2x+1 h
Solving an Equation for an Unknown Function Suppose that
g
(
x
)
=
2
x
+
1
h
(
x
)
=
4
x
2
+
4
x
+
7
Find a function
f
such that
f
∘
g
=
h
. (Think about what operation you would have to perform on the formula for g to end up with the formula for h.) Now suppose that
f
(
x
)
=
3
x
+
5
h
(
x
)
=
3
x
2
+
3
x
+
2
Use the same sort of reasoning to find a function g such that
f
∘
g
=
h
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