What is the inverse of the function f(x) = [(lnx)-5]/2

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the function f(x) = [ln(x)] - 5 /2

We need to find the inverse function f^-1 (x).

Let y= [ln(x) -5)/2

We will need to isolate x.

First we will multiply by 2.

==> 2y= ln x - 5

Now we will add 5 to both sides.

==> 2y + 5 = ln x

Now we will rewrite into exponent form.

==> x= e^(2y+5)

Now we will replace x and y.

==> y= e^(2x+5)

Then the inverse function is:

f^-1 (x) = e^(2x+5)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll interchange x by y:

x = (lny - 5)/2

We'll multiply both sides by 2:

2x = lny - 5

We'll add 5 both sides:

2x + 5 = ln y

We'll take antilogarithm:

f^-1(x) = y = e^(2x + 5)

The inverse function of the given function f(x) = [(lnx)-5]/2 is f^-1(x) = e^(2x + 5).

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