If the function f:[a, b] [- 3 4 , 1 2 ] defined by f(x)= | array ccc 1 & 1 & 1 1 & 1+ x & 1 1+ x & 1 & 1 array | is one-one and onto, then

Step-by-step solution

We have, f:(a, b) [ - 3 4 , 1 2 ] aligned & f(x)= | array ccc 1 & 1 & 1 1 & 1+ x & 1 1+ x & 1 & 1 array | & f(x)= | array ccc 1 & 0 & 0 1 & x & 0 1+ x & - x & - x array | & [C₃ C₃-C₁, C₂ C₂-C₁ ] & f(x)=- x x & f(x)=- 1 2 2 x & f(x) [ 3 4 , 1 2 ] aligned array rlrl & & - 3 4 & -1 2 2 x 1 2 & & -1 & 2 x 3 2 & - 4 & x 6 & & a & =- 4 , b= 6 array