Question

For what input value, the output of the function $g\left(x\right)=\frac{7}{2}x-\frac{49}{2}$ is $-\mathrm{17.5.}$

• A. $-2$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is D $2$

The given function is $g\left(x\right)=\frac{7}{2}x-\frac{49}{2}.$

Here, input is the independent variable, i.e., $x$ and output is the dependent variable $g\left(x\right).$

For output $=-17.5,$ i.e., $g\left(x\right)=-17.5,$ we need to solve for $x.$
$\Rightarrow -17.5=\frac{7}{2}x-\frac{49}{2}\Rightarrow -17.5+\frac{49}{2}=\frac{7}{2}x\Rightarrow \frac{7}{2}x=-\frac{175}{10}+\frac{49}{2}=-\frac{35\times 5}{2\times 5}+\frac{49}{2}$
(cancelling $5$ from numerator and denominator)
$\Rightarrow \frac{7}{2}x=-\frac{35}{2}+\frac{49}{2}=\frac{-35+49}{2}=\frac{14}{2}\Rightarrow x=2$

$\therefore$ For input as $2,$ the given function will produce an output of $-\mathrm{17.5.}$