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प्रश्न
The formula for converting from Fahrenheit to Celsius temperatures is y = `(5x)/9 - 160/9`. Find the inverse of this function and determine whether the inverse is also a function
उत्तर
Let f(x) = `(5x)/9 - 160/9`
= `(5x - 160)/9`
Given y = `(5x)/9 - 160/9`
= `(5x - 160)/9`
Then 9y = 5x – 160
⇒ 5x = 9y + 160
⇒ x = `(9y + 160)/5`
Let g(y) = `(9y + 160)/5`
g o f(x) = g(f(x))
= `g((5x - 160)/9)`
= `(9((5x - 160)/9) +160)/5`
= `(5x - 160 + 60)/5`
= `(5x)/5`
g o f(x) = x
f o g(y) = f(g(y))
= `f((9y + 160)/5)`
= `(5((9y + 160)/5) - 160)/9`
= `(9y + 160 - 160)/9`
= `(9y)/9`
f o g(y) = y
Thus g o f =Ix nd f o g = Iy
This shows that f and g are bijections and inverses of each other.
f–1(y = `(9y + 160)/5`
Replacing y by x we get f–1(x) = `(9x + 160)/5`
= `(9x)/5 + 32`
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