Given:


To find:
Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.
Solution:
We know that, two function are inverse of each other if:
 and
 and 
We have,


Now,
 
              ![[\because g(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20g%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)
 
            ![[\because f(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)


Similarly,
 
              ![[\because f(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)
 
            ![[\because g(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20g%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)


Since,  and
 and  , therefore, f(x) and g(x) are inverse of each other.
, therefore, f(x) and g(x) are inverse of each other.
 
        
             
        
        
        
654,035   654,035     654,035     654,035     654,035     654,035     654,035                          
        
             
        
        
        
<span>[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)</span><span>
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