Let f(x)=square root(x-4) + 3 . Find the inverse of f.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the inverse function of f(x) = sqrt(x - 4) + 3.

Let y = f(x)

y = sqrt(x - 4) + 3

=> y - 3 = sqrt(x - 4)

square both the sides

=> (y - 3)^2 = (x - 4)

=> (y - 3)^2 + 4 = x

interchange x and y

=> y = (x - 3)^2 + 4

The inverse function of f(x) = sqrt(x - 4) + 3 is f(x) = (x - 3)^2 + 4.

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the inverse of the function, we'll re-write the function, putting instead of f(x), y:

y = sqrt(x-4) + 3

We'll interchange x and y:

x = sqrt(y-4) + 3

We'll determine y from the expression above. We'll subtract 3 both sides:

x - 3 = sqrt(y-4)

We'll raise to square both sides:

(x-3)^2 = y - 4

We'll add 4 both sides and we'll apply symmetrical property:

y = (x-3)^2 + 4

The inverse function of f(x) is f^-1(x) = (x-3)^2 + 4.

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