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`f(x)={x+1, x |
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Answer» `f(g(x))={(g(x)+1",", g(x) lt0),({g(x)}^(2)",",g(x) ge0):}` `f(x)={(x^(3)+1",",x^(3) lt0", " x lt1),(2x-1+1",",2x-1 lt 0", "x ge1),((x^(3))^(2)",",x^(3) ge0", " x lt1),((2x-1)^(2)",",2x-1 ge 0", "x ge1):}` `={(x^(3)+1",", x lt0),(x^(6)",",0le x lt1),((2x-1)^(2)",", x ge1):}` Clearly, domain of function is R. For `x lt 0, x^(3) +1 in (-oo,1).` For `0le x lt 1, x^(6) in [0,1).` For ` x ge 1, (2x-1)^(2) in [1, oo).` Hence, the range is R. |
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