Question

The function $f\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x^{\circ }C$ to Fahrenheit units. Then at what ${}^{\circ }C$ both Celsius and Fahrenheit is same?

• A. ${32}^{\circ }C$
• B. $-{32}^{\circ }C$
• C. ${40}^{\circ }C$
• D. $-{40}^{\circ }C$

Answer 1

The correct option is D $-{40}^{\circ }C$

$f\left(x\right)=\frac{9x}{5}+32$
We know that the input is Celsius and output is Fahrenheit.
Let the temperature at which both the scale is same be $a$. Then
$f\left(a\right)=a\Rightarrow \frac{9a}{5}+32=a\Rightarrow \frac{9a}{5}-a=-32\Rightarrow \frac{4a}{5}=-32\Rightarrow a=-40$

Therefore, the required temperature is $-{40}^{\circ }C$.