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Text Solution

`f:RrarrR, f(x)=x^(4)+2x^(3)-x^(2)+1``f:RrarrR,f(x)=x^(3)+x+1``f:RrarrR,f(x)=sqrt(1+x^(2))``f:RrarrR, f(x)=x^(3)+2x^(2)-x+1`

Answer :

DSolution :

`f(x)=x^(4)+2x^(3)-x^(2)+1` is polynomial of even degree hence its range can't be R. <br> hence not surjective <br> `f(x)=x^(3) =x^(3)+x+1,f'(x)=3x^(2)+1` <br> implies monotonic hence bijective. <br> `f(x) -sqrt(1+x^(2)),` <br> neither surjective not injective. <br> `f(x)=x^(3)+2x^(2)-x+1` <br> `f'(x)=3x^(2)+4x-1 implies D=16+12gt0`. <br> Hence f(x) is non-monotonic cubic polynomial hence surjective but not injective**meaning of function**

**Modulus; signum; greatest integer and fractional part function**

**representation of function**

**Physical interpretation**

**Domain codomain and range of function**

**Graph of function: Vertical line test**

**Identity function**

**Explain Constant function with graph**

**Modulus function and properties**

**Greatest integer function and properties**