Which of the following is/are nonlinear function(s)?

y = 3 x + 2

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y = 3 x^{2} + 2 x

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y = 3 x^{3} + 2 x

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y = 3 x + 2 x

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Solution

The correct option is C $y = 3 x^{3} + 2 x$
A nonlinear function has the degree as 2 or greater than 2, but not less than 2.

Let's check the degree of all the functions.
$(A) y = 3 x + 2$
The power of $x$ in $3 x$ and $2$ are $1$ and $0$ respectively. So its highest power is $1.$
$\to Linear function$

$(B) y = 3 x^{2} + 2 x$
The power of $x$ in $3 x^{2}$ and $2 x$ are $2$ and $1$ respectively. So its highest power is $2.$
$\to Nonlinear function$

$(C) y = 3 x^{3} + 2 x$
The power of $x$ in $3 x^{3}$ and $2 x$ are $3$ and $1$ respectively. So its highest power is $3.$
$\to Nonlinear function$

$(D) y = 3 x + 2 x$
$\Rightarrow y = 5 x$
The power of $x$ in $5 x$ is $1.$
$\to Linear function$

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