Question

Please solve this step by step

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Answer 1

Step-by-step explanation

1) If IxI  =  2  then  x = 2   or   x = -2

∴ If x = 2   then value of f(x)  =  4(2) + 5  =  13

  If x = -2  then value of f(x)  =   I 4(-2) + 5 I   =  I -3 I  =  3

∴ Possible values of  f(x)  =  13 , 3

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2) If  f(x)  ≤  2 - x

   Then  either  ( 4x + 5 )  ≤  (2 - x)

              or        ( -4x + 5 )  ≤  (2 - x)

∴ If  ( 4x + 5 ) ≤ (2 - x)

then   (5x  + 3) ≤  0

∴ x ≤ -3/5

If  (-4x + 5)  ≤  (2 - x)

then  (-3x + 3)  ≤ 0

∴ x ≥ 1

∴ Values of x for which f(x)  ≤  (2 - x)  

=  ( -∞ , -3/5 ]  ∪  [ 1 , ∞ )

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3) I am not sure about this question as it is a bit ambiguous but still would like to attempt it :-

either  f(x)  =  (4x + 5)

or        f(x)   =  (-4x + 5)

∴ f(x)  + 2  =  (4x + 7)  or  (-4x + 7)

∴ (4x + 7)  = A  .... (1)  

  (-4x + 7) = A  .... (2)

∴ Adding Equations (1) and (2)  we get :-

  2A  =  14

∴ A    =  14 / 2

∴ A    =   7

∴ Possible values of A  = 7  ( I have just done what I thought was the method but still the 3rd question is a bit ambiguous )

∴ Possible Value of A  = 7.

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I Hope My Answer Helped You. Thank You !!!