Question

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

Answer 1

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.  

Composite functions 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), then substitute this in place of the x in function h(x).

Step 1

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

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

Step 2

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:

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

Answer 2

Answer:

true

Step-by-step explanation:

6(6(13x-2)

36(13x-2)

468x-72

please mark brainliest :D