Answer :
Answer:
[tex]g( x) = \frac{2}{3}x[/tex]
Step-by-step explanation:
Given:
Composite Function:
[tex]h( x)=f( g( x))[/tex]
Also,
[tex]h( x)=\frac{4}{3}x-1[/tex]
To find:
[tex]g( x ) = ?[/tex]
Solution:
First of all, let us learn about a composite function.
Composite function [tex]f( g( x))[/tex] means to write [tex]g( x)[/tex] in place of [tex]x[/tex] in the function [tex]f( x)[/tex].
Let [tex]g( x) = y[/tex]
So, [tex]f( g( x))[/tex] = [tex]f( y )[/tex].
Therefore,
[tex]h( x) =f( g( x)) = f( y)[/tex]
So, [tex]f( y) = 2y-1[/tex]
We have to solve for [tex]y[/tex] in terms of [tex]x[/tex] to find the value of [tex]g(x)[/tex]:
[tex]\Rightarrow \frac{4}{3}x-1 = 2y-1\\\Rightarrow 2y=\frac{4}{3}x\\\Rightarrow y = \frac{2}{3}x[/tex]
Hence, the answer is [tex]g( x ) = \frac{2}{3}x[/tex].
Checking whether the answer is correct or not:
[tex]f( g( x)) = f( \frac{2}{3}x) = 2\times \frac{2}{3}x -1 = \frac{4}{3}x-1[/tex]
which is [tex]h( x)[/tex].
Hence, our answer [tex]g( x ) = \frac{2}{3}x[/tex] is correct.
Answer:
If you using edgenuity, your answer is A. 2/3 times x
Step-by-step explanation:
Answers never mix up, so it will be A.