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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
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
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)
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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