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9. Let \(f(x) = 2x + 7\) and \(g(x) = 3x + c\) . Find c if \(f(g(x)) = g(f(x))\) for all .

 

10. The function f(x) satisfies

\(f(\sqrt{x + 1}) = \frac{1}{x}\)
for all \(x \ge -1,\) \(x\neq 0.\) Find f(2).

 

11. Let \(f(x) = 3x^2 - 4x\). Find the constant k such that \(f(x) = f(k - x)\) for all real numbers x .

 Feb 25, 2019
edited by Guest  Feb 25, 2019
edited by Guest  Feb 25, 2019
 #1
avatar+17253 
+1

9.     f (gx) = g (fx)

    2 (3x+c) + 7      = 3(2x+7) = c

    6x + 2c   + 7     =  6x + 21 + c

             c = 14

 Feb 25, 2019
 #2
avatar+98060 
+1

10.   f(2)   =  f ( √( x + 1] )    implies that

 

√ [ x + 1 ]  =  2   square both sides

 

x + 1 =  4

 

x = 3

 

So  

 

f(2)  =  1/3

 

cool cool cool

 Feb 25, 2019

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