### 5 Answers

- Ian HLv 72 months agoFavorite Answer
This tests if you understand that the intersection of the two graphs gives the solutions for both x and y. By sight that is x = 2, y = 3.

In case the graph does not guarantee enough acccuracy you can confirm that result by substitution.

When x = 2, f(x) = 3 and h(x) = 3, so the intersection was at (2, 3)

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- MangalLv 42 months ago
If two equations are plotted as graph, the intersection is the solution.

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- AlanLv 72 months ago
from looking at the picture alone,

you know the solution is somewhere near (2,3)

check it first

f(2) = (2+1) / (2-1) = 3

h(2) = (2-2)^2 + 3 = 3

so the picture told you the answer.

You don't even have to do the algebra (2,3)

if you did the algebra, it is little more complicated

(x+1)/(x-1) = (x-2)^2 +3

multiply both side by (x-1)

(x+1)= (x-2)^2(x-1) + 3(x-1)x

x+1 = (x^2 -4x + 4)(x-1) + 3x -1

x+1 = x^3 -4x^2 + 4x -x^2 +4x -4 -1 +3x

x^3 -5x^2 + 10x -6 = 0

rational roots theorem says possible answers

are +/-1 , +/- 2 , +/- 3 , and +/- 6

check shows

x =2 is the only solution

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- Mike JonesLv 62 months ago
" f(x) = h(x)? " is simply just asking where both functions are equal to each other, or in other words where they meet at the same coordinate. You can see clearly on this graph that your answer as an ordered pair is (2, 3) .

It doesn't look like they're requiring it but you can also solve this mathematically by setting the two functions equal to each other and solving for x:

(x + 1)/(x - 1) = (x - 2)² + 3

This would be your initial set-up.

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- LônLv 72 months ago
It's the coordinates of where the red line crosses the blue line...(2,3)

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