Question

A function f is defined by f(x) =2x-3
(I) find [f(0) +f(1) ]\2 (ii) find x such that f(x) =0 (iii) find x such that f(x) =x
(iv) find x such that f(x) =f(1-x)​

Answer 1

Answer :

(i) f(0) + f(1) ] / 2 = 1

(ii) x = 3/2

(iii) x = 3

(iv) x = 1/2

Solution :

Here ,

The given function is ;

f(x) = 2x - 3

(i) [ f(0) + f(1) ] / 2 = ?

=> [ f(0) + f(1) ] / 2 = [ (2•0 - 3) + (2•1 + 3) ] / 2

=> [ f(0) + f(1) ] / 2 = ( 0 - 3 + 2 + 3) / 2

=> [ f(0) + f(1) ] / 2 = 2/2

=> [ f(0) + f(1) ] / 2 = 1

(ii) If f(x) = 0 , then x = ?

=> f(x) = 0

=> 2x - 3 = 0

=> 2x = 3

=> x = 3/2

(iii) If f(x) = x , then x = ?

=> f(x) = x

=> 2x - 3 = x

=> 2x - x = 3

=> x = 3

(iv) If f(x) = f(1 - x) , then x = ?

=> f(x) = f(1 - x)

=> 2x - 3 = 2(1 - x) - 3

=> 2x = 2(1 - x)

=> x = 1 - x

=> x + x = 1

=> 2x = 1

=> x = 1/2