Question

The function h(x)=4/3x-1 represents the composite h(x)=f(g(x)).if f(x)=2x-1,what is g(x)

Answer 1

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.

Answer 2

Answer:

$g( x) = \frac{2}{3}x$

Step-by-step explanation:

Given:

Composite Function:

$h( x)=f( g( x))$

Also,

$h( x)=\frac{4}{3}x-1$

To find:

$g( x ) = ?$

Solution:

First of all, let us learn about a composite function.

Composite function $f( g( x))$ means to write $g( x)$ in place of $x$ in the function $f( x)$.

Let $g( x) = y$

So, $f( g( x))$ =  $f( y )$.

Therefore,

$h( x) =f( g( x)) = f( y)$

So, $f( y) = 2y-1$

We have to solve for $y$ in terms of $x$ to find the value of $g(x)$:

$\Rightarrow \frac{4}{3}x-1 = 2y-1\\\Rightarrow 2y=\frac{4}{3}x\\\Rightarrow y = \frac{2}{3}x$

Hence, the answer is $g( x ) = \frac{2}{3}x$.

Checking whether the answer is correct or not:

$f( g( x)) = f( \frac{2}{3}x) = 2\times \frac{2}{3}x -1 = \frac{4}{3}x-1$

which is $h( x)$.

Hence, our answer $g( x ) = \frac{2}{3}x$ is correct.