Question

Identify the nonlinear function(s).

• A. $y=x^e-e$
• B. $y=x^{(2-\frac{1}{2})-1.5}-x^{\frac{(2-\frac{1}{2})}{1.5}}$
• C. $f\left(t\right)=4t^3-2t^2-t$
• D. $xy=1$

Answer 1

Answer: (A), (C), (D)

$xy=1$

Graphically: A function, whose graph is not a straight line and passes vertical line test, is called a non-linear function.

By equation:
If a function in the form of $y=f\left(x\right)$ has atleast one term in which exponent of $x$ is other than $0$ or $1$ is called non-linear function.

Let's verify each given function.

$y=x^e-e$
Here, $e$ is a constant whose approximate value is $\mathrm{2.72.}$
Hence, this function is non-linear.

$y=x^{(2-\frac{1}{2})-1.5}-x^{\frac{(2-\frac{1}{2})}{1.5}}$
$\Rightarrow y=x^{1.5-1.5}-x^{\frac{1.5}{1.5}}$
$\Rightarrow y=x^0-x^1$
$\Rightarrow y=1-x$
This is a linear function.

$f\left(t\right)=4t^3-2t^2-t$
Here, the dependent variable is $t.$
Exponents of $t$ are $3,2$ and $1.$
$\therefore$ This is a non-linear function.

$xy=1$
$\Rightarrow y=\frac{1}{x}$
$\Rightarrow y=x^{-1}$
$\therefore$ This is also a non-linear function.