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2 years ago

13

Pls help! i need an explanation and the steps that show how it’s solved too. tysm!

2 answers:

sergey [27]2 years ago

7 0

Answer:

True

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}$

$h(h(g(x)))$ is a composite function.

<u>Composite functions</u> are when the output of one function is used as the input of another.

Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), <em>then </em>substitute this in place of the x in function h(x).

<u>Step 1</u>

Substitute the function g(x) in place of the x in function h(x):

$\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}$

<u>Step 2</u>

Now substitute the above in place of the x in function h(x):

$\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}$

Therefore, the statement is true.

To carry out the composite function in one step:

$\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}$

Julli [10]2 years ago

6 0

Answer:

true

Step-by-step explanation:

6(6(13x-2)

36(13x-2)

468x-72

please mark brainliest :D

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