(a) If g ( x ) = 2 x + 1 and h ( x ) = 4 x 2 + 4 x + 7 , find a function f such that f ∘ g = h . (Think about what operations you would have to perform on the formula for g to end up with the formula for h .) (b) If f ( x ) = 3 x + 5 and h ( x ) = 3 x 2 + 3 x + 2 , find a function g such that f ∘ g = h .
(a) If g ( x ) = 2 x + 1 and h ( x ) = 4 x 2 + 4 x + 7 , find a function f such that f ∘ g = h . (Think about what operations you would have to perform on the formula for g to end up with the formula for h .) (b) If f ( x ) = 3 x + 5 and h ( x ) = 3 x 2 + 3 x + 2 , find a function g such that f ∘ g = h .
Solution Summary: The author explains how to find the function f such that fog=h.
(a) If
g
(
x
)
=
2
x
+
1
and
h
(
x
)
=
4
x
2
+
4
x
+
7
, find a function f such that
f
∘
g
=
h
. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
(b) If
f
(
x
)
=
3
x
+
5
and
h
(
x
)
=
3
x
2
+
3
x
+
2
, find a function g such that
f
∘
g
=
h
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.