1. Tardigrade
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  3. Mathematics
  4. The function f: R→ R is defined by f(x) = begincases 12x+5, textif x > 1 [2ex] x-4 , textif x le 1 endcases Which of the following is false?

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Q. The function $f : R\to R$ is defined by
$f(x) = \begin{cases} 12x+5, & \text{if $x >\,1$} \\[2ex] x-4 , & \text{if $x \le\,1$} \end{cases}$
Which of the following is false?

Relations and Functions

Solution:

$f\left(0\right)=0-4=-4$,
$f\left(-\frac{1}{2}\right)=-\frac{1}{2}-4$
$=-\frac{9}{2}$,
$f\left(3\right)=12\left(3\right)+5=41, f\left(-5\right)=-5-4$
$=-9\ne9$.