Relations and Functions — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
Question
Let f: R $\rightarrow$ R be defined as$f\left( x \right){\text{ }} = {\text{ }}{x^4}$. Choose the correct answer.
✓
Answer
Since f (-1) = 1, f (1) = 1, f(-2) =16 , f(2) = 16. Thus, 1 and -1 have the same image. Similarly, 2 and -2 also have the same image. So, f is many-one function. Also, for all $y \in R,{y^{\frac{1}{4}}}$ is a real number. Thus, for all y $\in$ R.There exists x = ${y^{\frac{1}{4}}}$ in R such that f(x) = ${x^4} = y.$ Therefore, f is onto. So, f is many one and onto.
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