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Annette [7]
3 years ago
15

What is (f ° g)(2) and (g ° f)(2) with the set of points f: {(0,4), (1,2), (2,0), (3,2), (4,4)} and g: {(0,4), (1,3), (2,2), (3,

1), (4,0)}
Mathematics
1 answer:
kumpel [21]3 years ago
7 0

Answer:

\large\boxed{(f\circ g)(2)=0}\\\boxed{(g\circ f)(2)=4}

Step-by-step explanation:

f:\{(0,4), (1,2), \underline{(2,0)}, (3,2), (4,4)\}\\\\g:\{\underline{(0,4)}, (1,3), \underline{(2,2)}, (3,1), (4,0)\}\\\\(f\circ g)(x)=f\bigg(g(x)\bigg)\\\\g(2)=2\qquad/from\ (2,2)/\\f\bigg(g(2)\bigg)=f(2)=0\qquad/from\ (2,0)/\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(2)=0\qquad/from\ (2,0)/\\g\bigg(f(2)\bigg)=g(0)=4\qquad/from\ (0,4)/

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Step-by-step explanation:

Given: Total solution required =  130 milliliters

Let x = Amount of 35% solution (in milliliters).

Then, Amount of 87% solution required = 130 - x

As per given,

Concentration = 0.35x +0.87(130-x)=0.47(130)

0.35x +113.1-0.87x=61.1\\\\\Rightarrow\ -0.87x+0.35x=61.1-113.1\\\\\Rightarrow\ -0.52 x= -52\\\\\Rightarrow\ x=\dfrac{52}{0.52}=100

Hence, Amount of 35% solution required = 100 milliliters

Amount of 87% solution required  = 130-100 milliliters =30 milliliters

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