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find the inverse formula for the function f(x)= 3x-7

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annaball111 | Student, College Freshman | eNotes Newbie

Posted November 29, 2010 at 7:39 AM via web

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find the inverse formula for the function f(x)= 3x-7

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

Posted November 29, 2010 at 7:41 AM (Answer #1)

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Given the function f(x) = 3x - 7.

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

First we will rewrite.

Let y = 3x - 7.

The goal is to isolate x on one side.

Now we will add 7 to both sides.

==> y + 7 = 3x - 7 + 7

==> y + 7 = 3x

Now we will divide by 3:

==> (y+ 7) /3 = x

==> x = ( y+ 7) /3

Now we will rewrite x as y and y as x:

==> y= (x+ 7) /3

==> Then the inverse of f(x) = (x+ 7) /3

==> f^-1 ( x) = (x+ 7) /3

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neela | High School Teacher | Valedictorian

Posted November 29, 2010 at 10:57 AM (Answer #2)

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To find the inverse of f(x) = 3x-7.

Let the inverse of f(x) = 3x-7 be f^-1 (x) = y.

Then by definition, x = f(y).

So  x= 3y-7.

We add 1 to both sides and solve for y:

x+7 = 3y.

We divide both sides by 3:

(x+7)/3 = y.

Therefore y = (x+7)/3.

Therefore y = f^-1(x) = (x+7)/3.

Therefore f^-1 (x) = (x+7)/3 is the inverse of f(x) = 3x-7.

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giorgiana1976 | College Teacher | Valedictorian

Posted November 29, 2010 at 6:30 PM (Answer #3)

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To determine the inverse function means to determine x with respect to y, from the given expression of f(x).

We'll note f(x) = y and we'll re-write the equation:

y = 3x - 7

We'll use the symmetryc property:

3x - 7 = y

We'll isolate 3x to the left side. For this reason, we''' add 7 both sides:

3x = y + 7

Now, we'll divide by 3 both sides to get x

x = (y+7)/3

The inverse function is f(y) = (y+7)/3

By definition, we'll write the inverse function as:

f^-1(x) = (x+7)/3

f^-1(x) = x/3 + 2.(3)

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Wiggin42 | TA , Grade 11 | Valedictorian

Posted May 31, 2014 at 1:42 AM (Answer #4)

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We need to find the inverse formula for the function f(x)= 3x-7

Inverse functions are reflections of the original function over the line y = x. As such, to find the inverse we can switch the x's for the y's like so : 

y = 3x - 7  (original)

x = 3y - 7  (inverse)

We want the inverse to be a function of x, not y, so we solve for y: 

y = ( x  + 7 )/3

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