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f(x) = \( \sqrt{2x-5}\)

g(x) = \( {10 \over x}\frac{}{}\)

solve the equation fg(x) = 5 

 Aug 16, 2019
 #1
avatar+104899 
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fg (x)   =    5

 

√[2x - 5]  / 10 / x     = 5      multiply  both sides  by x

 

√[2x - 5] * 10  = 5x              divide both sides by 5

 

2√[2x -5]  = x                    square both sides

 

4 (2x - 5)  = x^2               rearrange as

 

x^2  - 8x  + 20   = 0       complete the  square on x

 

x^2  - 8x + 16  =  -20 + 16

 

(x - 4)^2  = -4                take both roots

 

x - 4  = ±√[-4]

 

x - 4= ±2i

 

x = 4 ± 2i

 

cool cool cool

 Aug 16, 2019

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