The maximum value of the function a x+ b x is

Step-by-step solution

The function f(x) = a x + b x can be expressed as a single trigonometric function using the identity for R (x + ) . Let a = R and b = R . By squaring and adding these expressions, we obtain a^2 + b^2 = R^2( ^2 + ^2 ) = R^2 , so R = a^2 + b^2 . Substituting into the original function yields f(x) = R( x + x ) = R (x + ) . Since (x + ) 1 , the maximum value of f(x) is R = a^2 + b^2 . The correct option is A .