Consider the functions defined by f ( x ) = 6 x − 2 , g ( x ) = − x 2 − 4 x + 1 , h ( x ) = 7 , and k ( x ) = | x − 2 | . For Exercises 21-52, find the following. (See Examples 3-4 .) g ( a )
Consider the functions defined by f ( x ) = 6 x − 2 , g ( x ) = − x 2 − 4 x + 1 , h ( x ) = 7 , and k ( x ) = | x − 2 | . For Exercises 21-52, find the following. (See Examples 3-4 .) g ( a )
Solution Summary: The author explains the formula used to calculate the value of g(a).
Consider the functions defined by
f
(
x
)
=
6
x
−
2
, g
(
x
)
=
−
x
2
−
4
x
+
1
,
h
(
x
)
=
7
,
and
k
(
x
)
=
|
x
−
2
|
. For Exercises 21-52, find the following. (See Examples 3-4.)
Consider the function h(x) = (2x3 - 5)5 + (2x3 - 5)4. Write h(x) as a composite function, f ( g (x)).
Determine if the functions in each pair are equivalent. Provide mathematical proof or
justification for your answer – algebraic or by substituting x = 0.
a) f (x) = (-5x² + 100x + 1000) – (-5x² + 75x + 1200) and g(x) = 25x – 200
b) f(x) = (2x – 1) + (x – 2) – (x – 3) and g(x) = (3x – 2) – (2x + 3) – (-x – 1)
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