If f (x)= ⁻¹ ( 2 3^x 1+9^x ) , then f ^ ( 1 2 ) equals

Step-by-step solution

aligned & f (x)= ⁻¹ ( 2.3^x 1+9^x )= ⁻¹ ( 2.3^x 1+ (3^x )^2 ) & Put 3^x= = ⁻¹ (3^x ) & f (x)= ⁻¹ ( 2 1+ ^2 ) &= ⁻¹( 2 ) &=2 aligned aligned & f (x)=2 ⁻¹ (3^x ) & f ^ (x)=2 1 1+ (3^x )^2 3^x 3 f ^ ( 1 2 ) & =2 1 1+ (3^ 1 2 )^2 3^ 1 2 3 & = 1 2 3 3= 3 3 aligned