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Statement-1: If `f:R to R and g:R to R ` be two functions such that `f(x)=x^(2) and g(x)=x^(3)`, then fog (x)=gof (x). Statement-2: The composition of functions is commulative.A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - C We have `fog(x)=f(g(x))=f(x^(3))^(2)=x^(6)` `and gof(x)=g(f(x))=g(x^(2))=(x^(2))^(3)=x^(6)` `therefore fog(x)=gof(x)` So, statement-1 is true. If f(x`=x^(2) and g(x)=sin x` Then, `fog(x)=sin^(2)x and gof (x)=sin x^(2)` `therefore fog(x) ne gof (x)`. So, the composition of functions is not commutative. Hence, statement-2 is false. |
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