Question

If f(x) = x² −2x+2 , evaluate f(2) – f(1) +f (1/2)

Answer 1

Answer :

Given that,

f (x) = x² - 2x + 2

Now, f (2) - f (1) + f (1/2)

= {2² - 2 (2) + 2} - {1² - 2 (1) + 2} + {(1/2)² - 2 (1/2) + 2 }

= (4 - 4 + 2) - (1 - 2 + 2) + (1/4 - 1 + 2)

= 2 - 1 + 1 + 1/4

= 2 + 1/4

= (8 + 1)/4

= 9/4

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Answer 2

Given,

f(x) = x² −2x+2

To find,

The value of f(2) – f(1) +f (1/2).

Solution,

The value of f(2) – f(1) +f (1/2) will be 9/4.

We can easily solve this problem by following the given steps.

Now, to find the value of f(2) – f(1) +f (1/2), we will first find the values of f(2), f(1), and f(1/2) separately and will later put these values in the given expression.

According to the question,

f(x) = x² −2x+2

Finding the value of f(2),

f(2) = (2)²-2(2)+2

f(2) = 4-4+2

f(2) = 6-4

f(2) = 2

Finding the value of f(1),

f(1) = (1)²-2(1)+2

f(1) = 1-2+2

f(1) = 3-2

f(1) = 1

Finding the value of f(1/2),

f(1/2) = (1/2)²-2(1/2)+2

f(1/2) = 1/4 -1+2

f(1/2) = (1-4+8)/4 [Taking the LCM of 4 and 1]

f(1/2) = (9-4)/4

f(1/2) = 5/4

Now, putting these values in

f(2) – f(1) +f (1/2)

2-1+5/4

Taking the LCM of 1, 1 and 4,

(8-4+5)/4

(13-4)/4

9/4

Hence, the value of f(2) – f(1) +f (1/2) is 9/4.