![\bf f(x)=\cfrac{2x-3}{x+1}~\hspace{10em}g(x)=\cfrac{x+3}{2-x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(~~g(x)~~)\implies \cfrac{2[g(x)]-3}{[g(x)]+1}\implies \cfrac{2\left( \frac{x+3}{2-x} \right)-3}{\left( \frac{x+3}{2-x} \right)+1}\implies \cfrac{\frac{2x+6}{2-x}-3}{\frac{x+3}{2-x}+1} \\\\\\ \cfrac{\frac{2x+6-6+3x}{2-x}}{\frac{x+3+2-x}{2-x}}\implies \cfrac{2x+6-6+3x}{2-x}\cdot \cfrac{2-x}{x+3+2-x}\implies \cfrac{5x}{5}\implies x](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%5Ccfrac%7B2x-3%7D%7Bx%2B1%7D~%5Chspace%7B10em%7Dg%28x%29%3D%5Ccfrac%7Bx%2B3%7D%7B2-x%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Af%28~~g%28x%29~~%29%5Cimplies%20%5Ccfrac%7B2%5Bg%28x%29%5D-3%7D%7B%5Bg%28x%29%5D%2B1%7D%5Cimplies%20%5Ccfrac%7B2%5Cleft%28%20%5Cfrac%7Bx%2B3%7D%7B2-x%7D%20%5Cright%29-3%7D%7B%5Cleft%28%20%5Cfrac%7Bx%2B3%7D%7B2-x%7D%20%5Cright%29%2B1%7D%5Cimplies%0A%5Ccfrac%7B%5Cfrac%7B2x%2B6%7D%7B2-x%7D-3%7D%7B%5Cfrac%7Bx%2B3%7D%7B2-x%7D%2B1%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B%5Cfrac%7B2x%2B6-6%2B3x%7D%7B2-x%7D%7D%7B%5Cfrac%7Bx%2B3%2B2-x%7D%7B2-x%7D%7D%5Cimplies%20%5Ccfrac%7B2x%2B6-6%2B3x%7D%7B2-x%7D%5Ccdot%20%5Ccfrac%7B2-x%7D%7Bx%2B3%2B2-x%7D%5Cimplies%20%5Ccfrac%7B5x%7D%7B5%7D%5Cimplies%20x)
![\bf \rule{34em}{0.25pt}\\\\ g(~~f(x)~~)\implies \cfrac{[f(x)]+3}{2-[f(x)]}\implies \cfrac{\frac{2x-3}{x+1}+3}{2-\frac{2x-3}{x+1}}\implies \cfrac{\frac{2x-3+3x+3}{x+1}}{\frac{2x+2-(2x-3)}{x+1}} \\\\\\ \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-(2x-3)}\implies \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-2x+3} \\\\\\ \cfrac{5x}{5}\implies x](https://tex.z-dn.net/?f=%5Cbf%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Ag%28~~f%28x%29~~%29%5Cimplies%20%5Ccfrac%7B%5Bf%28x%29%5D%2B3%7D%7B2-%5Bf%28x%29%5D%7D%5Cimplies%20%5Ccfrac%7B%5Cfrac%7B2x-3%7D%7Bx%2B1%7D%2B3%7D%7B2-%5Cfrac%7B2x-3%7D%7Bx%2B1%7D%7D%5Cimplies%20%5Ccfrac%7B%5Cfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%7D%7B%5Cfrac%7B2x%2B2-%282x-3%29%7D%7Bx%2B1%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%5Ccdot%20%5Ccfrac%7Bx%2B1%7D%7B2x%2B2-%282x-3%29%7D%5Cimplies%20%5Ccfrac%7B2x-3%2B3x%2B3%7D%7Bx%2B1%7D%5Ccdot%20%5Ccfrac%7Bx%2B1%7D%7B2x%2B2-2x%2B3%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B5x%7D%7B5%7D%5Cimplies%20x)
and in case you recall your inverses, when f( g(x) ) = x, or g( f(x) ) = x, simply means, they're inverse of each other.
Okay so. Here's what it looks like : TRUCK PLUS: $25 is the fee upfront. so no matter what your GOING to pay $25 for using the company. Next 15 cents for every mile driven. So if the truck were to drive 3 miles it would be $.45 cents
NEED-A-TRUCK : Same thing. You have to pay $25 no matter what. But for this company you have to pay $.10 per mile. COST PER MILE means that basically the more miles you drive, the more cents you have to pay. Does that make sense? <span />
Answer:
10.2
How I found this answer:
4+6=10
3-1=2
10^2+2^2=104
The square root of 104 is 10.1980390272, which can be rounded to 10.2
The answer is 4. Hope this helps!
-Belle
By evaluating, we will see that for x = 7 h(x) exceeds g(x).
<h3>
For which value of x does h(x) first exceed g(x)?</h3>
We have:
h(x) = 2*(2)^x
g(x) = 22x - 4
Now we can evaluate both function in the different options:
h(5) = 2*(2)^5 = 64
g(5) = 22*5 - 4 = 106
We can see that for x = 5, h(x) does not exceed g(x), let's try the next one.
h(6) = 2*(2)^6 = 128
g(6) = 22*6 - 4 = 128
So, for x = 6 both functions have the same output, then for x = 7 we will see that h(x) exceeds g(x).
The correct option is B.
If you want to learn more about functions:
brainly.com/question/4025726
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