JEE Main2014MathematicsFunctionsActual

If f(x)=x^2-x+5, x> 1 2 , and g ( x ) is its inverse function, then g ^ (7) equals:

Options

A- 1 3
B1 13
C1 3
D- 1 13

Correct answer

C. 1 3

Step-by-step solution

f(x)=y=x^2-x+5 aligned &x^2-x+ 1 4 - 1 4 +5=y & (x- 1 2 )^2+ 19 4 =y & (x- 1 2 )^2=y- 19 4 &x- 1 2 = y- 19 4 aligned aligned &x= 1 2 y- 19 4 & As x> 1 2 &x= 1 2 + y- 19 4 &g(x)= 1 2 + x- 19 4 &g^ (x)= 1 2 x- 19 4 aligned g^ (7)= 1 2 7- 19 4 = 1 2 28-19 2 = 1 3

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