Answer to Question #144455 in Algebra for Ankita Sonawane

Question

Find all points (x, y) where the functions f(x), g(x), h(x) have the same value :
f(x) = 2x−5 + 3 , g(x) = 2x − 5 , h(x) = (8/x)+ 10

Answer 1

f(x)=2x-5+3 = 2x -2

g(x)= 2x-5

h(x) =8/x +10

To find the point they all have the same value, we have to equate them together

However your f(x) you inputed seem to be wrong because we won't have X value for the function with g(x). So let's work with what you provided. I can't assume any value

f(x)=g(x)=h(x)

f(x) =g(x) won't give us any X value

f(x) = h(x)

2x-2 = 8/x +10

2x = 8/x +12

2x² =8 + 12x

2x²-12x-8=0

x = -0.606 or 6.606

y= 2x-2 = 2(-0.606)-2 or 2(6.606)-2

y=-1.212 or 11.212

The values here are (-0.606, -1.212) (6.606,11.212)

g(x) = h(x)

2x - 5 = 8/x +10

2x = 8/x +15

2x²= 8 + 15x

2x² - 15x -8=0-

x = -0.5 or 8

y= 2x-5 = -6 or 11

The values at this point = (-0.5,-6) (8,11)