A temperature change can be expressed through three functions

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

A temperature change can be expressed through three functions. • Conversion from Fahrenheit to Celsius:

C(t)=\dfrac{5}{9}(t-32)

. • Conversion from Celsius to Fahrenheit:

F(u)=\dfrac{9}{5}u+32

. • Conversion from Celsius to Kelvin:

S(v)=v+273

. (i) Verify that

F\bigl(C(t)\bigr)=t

for every real

t

. (ii) Simplify the composition

C\bigl(F\bigl(S\bigl(C(t)\bigr)\bigr)\bigr)

step by step until a final explicit function of

t

is obtained. (iii) Using your simplified result, find the Kelvin temperature corresponding to

95^{\circ}\text{F}