Question

Given: f(X) = 2x^n+a , if : f(2)=26 and f(4)=138 , than : f(3) = ______

A. 56
B. 82
C. 64
D. 122
.........Full explain Please...​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of f(3) is (C) 64.

Given: f(X) = 2x^n + a ,

           f(2) = 26 and f(4) = 138

To Find: The value of f(3).

Solution:

To find the solution to this question, we need to first find the values of  'a' and 'n'. We are given,

          f(X) = 2x^n+a , and  f(2)=26 and  f(4)=138 ,

So substituting X = 2 in f(X), we get;

          f(2) = 2 × 2^n + a

     ⇒ 26 = 2^(n+1) + a                                         ......(1)

Again substituting X = 4 in f(X), we get;

        f(4) = 2 × 4^n + a

     ⇒ 138 = 2^(2n + 1) + a                                    .....(2)

Subtracting (2) from (1), we get;

       2^(2n + 1) + a - 2^(n+1) - a  =  138 - 26

  ⇒  2 × [ 2^2n - 2^n ] = 112

  ⇒  2^2n - 2^n - 56 = 0

Now, let us take 2^n = t, so rewriting the above equation, we get,

       t² - t - 56 = 0

   ⇒ t² - 8t + 7t - 56 = 0

   ⇒ t ( t - 8 ) + 7 ( t - 8 ) = 0

   ⇒ t = -7 , 8

So, t ≠ -7, taking t = 8,

   ⇒ 2^n = 8

   ⇒ 2^n = 2^3

   ⇒ n = 3

So, putting n = 3 in (1), we get;

        2^(n+1) + a = 26

   ⇒ 2^(3+1) + a = 26

   ⇒ a = 26 -16

   ⇒ a = 10

Hence, the value of n = 3 and a = 10

So, f(3) = 2 × 3^3 + 10

           = 54 + 10

           = 64

Hence, the value of f(3) is (C) 64.

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