Question

A function f is defined by f(x)=3-2x. find x such that f(x^2)=(f(x))^2




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Answer 1

Answer :

x = 1

Solution :

• Given : f(x) = 3 - 2x

• To find : The value of x if f(x²) = (f(x))²

Now ,

=> f(x²) = (f(x))²

=> 3 - 2x² = (3 - 2x)²

=> 3 - 2x² = 3² + (2x)² - 2•3•2x

=> 3 - 2x² = 9 + 4x² - 12x

=> 4x² + 2x² - 12x + 9 - 3 = 0

=> 6x² - 12x + 6 = 0

=> 6(x² - 2x + 1) = 0

=> x² - 2x + 1 = 0

=> x² - 2•x•1 + 1² = 0

=> (x - 1)² = 0

=> x = 1 , 1

=> x = 1

Hence , x = 1 .