CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$f:R\rightarrow R$$ is given by $$f(x)={x}^{3}$$, write $${f}^{-1}(1)$$.


Solution

$$f:R\rightarrow R$$ is given by $$f(x)=x^3$$.

Let $$f^{-1}(1)=x$$                  ---- ( 1 )
$$\Rightarrow$$  $$f(x)=1$$
$$\Rightarrow$$  $$x^3=1$$  ...................[ Given ]
$$\Rightarrow$$  $$x^3-1=0$$
$$\Rightarrow$$  $$(x-1)(x^2+x+1)=0$$ ...................[ Since, $$a^3-b^3=(a+b)(a^2+ab+b^2)$$ ]

Value of $$x$$ of $$x^2+x+1$$ will be complex number.

As $$x\in R$$, then $$x^2+x+1=0$$ is not possible.
$$\Rightarrow$$  $$x-1=0$$
$$\Rightarrow$$  $$x=1$$
From ( 1 ),
$$\Rightarrow$$  $$f^{-1}(1)=\{1\}$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image