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The function $f: R \rightarrow R$ defined by $f(x)=\left(x^{2}+1\right)^{35}$ for all $x$ $\in R$ is
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neither one-one nor onto
$f(-1)=f(1)=2^{35}$
Here, two real numbers 1 and $-1$ have the same image. So, the function is not one-one and let $y=\left(x^{2}+1\right)^{35}$
$\Rightarrow x=\sqrt{(y)^{1 / 35}-1}$
Thus, every real number has no pre image. So, the function is not onto. Hence, the function is neither one-one nor onto.
Here, two real numbers 1 and $-1$ have the same image. So, the function is not one-one and let $y=\left(x^{2}+1\right)^{35}$
$\Rightarrow x=\sqrt{(y)^{1 / 35}-1}$
Thus, every real number has no pre image. So, the function is not onto. Hence, the function is neither one-one nor onto.
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