Indicate a method to find the inverse of the function f(x)=square root(x-2)/5?

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Let f(x) = y = [sqrt (x - 2)]/5

express x in terms of y

y = [sqrt (x - 2)]/5

=> 5y = sqrt (x - 2)

=> 25y^2 = (x - 2)

=> x = 25*y^2 + 2

interchange x and y

=> y = 25*x^2 + 2

**The inverse of f(x) , f^-1(x) = 25x^2 + 2**

Whenever we want to determine the inverse function, we'll have to write x with respect to y.

Let f(x) = y and we'll re-write:

y = sqrt(x-2)/5

We'll multiply both sides by 5:

5y = sqrt(x-2)

We'll raise to square both sides, to eliminate the square root:

(5y)^2 = x-2

We'll use the symmetric property:

x-2 = 25y^2

We'll add 2 both sides:

x = 25y^2 + 2

**Therefore, the required inverse function is: f^-1(x) = 25x^2 + 2.**

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