SOLUTION: Suppose H(x)=√6x-1.
Find two functions f and g such that
(f °g)(x) = H(x)
f(x) =
g(x) =
I don't understand how I figure out the functions.
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Functions
-> SOLUTION: Suppose H(x)=√6x-1.
Find two functions f and g such that
(f °g)(x) = H(x)
f(x) =
g(x) =
I don't understand how I figure out the functions.
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Question 1168502: Suppose H(x)=√6x-1.
Find two functions f and g such that
(f °g)(x) = H(x)
f(x) =
g(x) =
I don't understand how I figure out the functions. Answer by greenestamps(13200) (Show Source):
If you use the "√" symbol in your post, use parentheses to make the meaning clear.
Is H(x) equal to √6x-1 = ?
Or is it equal to √(6x-1) = ?
I suspect it is supposed to be the second; but it could be either one.
I will go ahead and explain how to answer the question if .
If it is the other one, you can use my discussion below to answer the question for that other case.
Look at the function and see what it does to the input value x:
(1) multiply by 6;
(2) take the square root; and
(3) subtract 1
To make the function H(x) a composition of two function f(x) and g(x), simply condense that sequence of three operations into a sequence of two operations, keeping all the operations in the original order.
There are two possibilities:
One choice is to combine steps (1) and (2):
(1) multiply by 6 and take the square root; and
(2) subtract 1
Then the function g(x) is the first of those steps: ;
and the function f(x) is the second:
ANSWER (one possibility): and
The other choice is to keep step 1 by itself and combine steps 2 and 3:
(1) multiply by 6; and
(2) take the square root and subtract 1
Then the function g(x) is ;
and the function f(x) is
