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Let `f(x)=(x+1)^2-1, xgeq-1.`Then the set `{x :f(x)=f^(-1)(x)}`is`{0,1,(-3+isqrt(3))/2,(-3-isqrt(3))/2}`(b) `{0,1,-1``{0,1,1}`(d) `e m p t y`A. `{0,-1,(-3+isqrt(3))/(2),(-3-isqrt(3))/(2)}`B. `{0,1,-1}`C. `{0, -1}`D. empty |
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Answer» Correct Answer - C Since `f(x) = (x+1)^(2)-1` is continuous function, solution of `f(x)=f^(-1)(x)` lies on the line `y=x`. Therefore, `f(x)=f^(-1)(x)=x` ` or (x+1)^(2)-1=x` ` or x^(2)+x=0` i.e., ` x=0 or -1` Therefore, the required set is `{0,-1}.` |
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