Question

Let f(x) = 2x – x 2 , find (i) f(1) (ii) f(x + 1)
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Answer 1

Given : Function is f(x) = 2x - x²

To find : Values of f(1), f(x+1)

Solution :

To find the value of f(1) just replace the variable x from the function with 1.

→ f(x) = 2x - x²

→ f(1) = 2(1) - (1)²

→ f(1) = 2 - 1

→ f(1) = 1

So f(1) = 1

To find the value of f(x + 1) replace the variable x from the function with x + 1.

→ f(x) = 2x - x²

→ f( x + 1 ) = 2 ( x + 1 ) - ( x + 1 ) ²

→ f(x + 1 ) = 2 x + 2 - [ x² + 2x + 1 ]

→ f( x + 1 ) = 2x + 2 - x² - 2x - 1

→ f( x + 1 ) = 1 - x²

So f( x + 1 ) = 1 - x²