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denpristay [2]
3 years ago
13

F:x→(x+1/x+3), x≠3 and g:x→(6/x-2), x≠2, find f²(4) and g²(1/2)​

Mathematics
1 answer:
Sveta_85 [38]3 years ago
3 0

Answer:

f^2(4) =  (\frac{25}{49})\\g^2(\frac{1}{2} ) = 16

Step-by-step explanation:

Here, given:

f(x) = (\frac{x+1}{x+3} ), g(x) = (\frac{6}{x-2} )

Now, here  to find the values of f^2(4), g^2(\frac{1}{2})

As we know: f^n(x) = (f(x))^n

Now, substituting x = 4 in f(x):

f(4) = \frac{4 +1}{4+3}  = \frac{5}{7} \\\implies f^4 = (f(4))^2  =  (\frac{5}{7} )^2 = \frac{25}{49} \\\implirs f^{(4)} =  ( \frac{25}{49})

Now, substituting x = 1/2 in g(x):

g(\frac{1}{2} ) = \frac{6}{\frac{1}{2}-2}  = \frac{6}{-\frac{3}{2}} \\\\ g(\frac{1}{2} )  = -6\times (\frac{2}{3} )  = -4\\\implies g^2{(\frac{1}{2})   = ( g(\frac{1}{2} ))^2  =  (-4 )^2 =16 \\\\\implies g^2{(\frac{1}{2})  =  16

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