g(x) is an anti derivative of f(x)=1+2^x 2 and the graph of y=g(x) passes through (-1, 1 2 ) . Then the curve meets the Y - axis at

Step-by-step solution

f(x)=1+2^x 2 aligned & f(x)= (1+2^x 2 ) d x & g(x)=x+ 2^x 2 2 +c aligned g (x)=x+2^x+c y=x+2^x+c ...(i) Equation (i) passes through (-1, 1 2 ) 1 2 =-1+2⁻¹+c c=1 Putting value of c in eq ^ n (i), we get y=x+2^x+1 ...(ii) When curve (ii) meets y -axis: x=0 y=0+2^ +1=2 Curve meet y -axis at the point (0,2)