What is the inverse of the function f(x) = 2x + 1? 1
o h(x) = 5x-
2x +
O h(x) = 1
3x-2
N/" Nr
Oh(x) =
O h(x) = x + 2

(x) =

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

= x

Change y back into terms of x with x = (x) , so

(x) =

 " f⁻¹(x) = (x-1)/2  ";  or, write as:

              " f⁻¹(x) = (x/2) - (1/2) " .

Step-by-step explanation:

Given:   f(x) = 2x + 1 ;  Find the inverse:

1)  Rewrite as y = 2x + 1 ;

2) Replace the "x" with "y" ; and the "y" with "x" ; and rewrite:

         x = 2y + 1 ;

3)  Now, "solve"; with "y" standing alone as a single, isolated variable on the left side of the equation, with an "equals" sign following the "y" :

         x = 2y + 1 :

Subtract "1" from each side of the equation:

         x - 1 = 2y + 1 - 1 ;

to get:

         x - 1 = 2y ;

↔  Rewrite as :

2y = x - 1 ;

Now, divide each side of the equation by "2" ;

  to isolate "y" on the left-hand side of the equation;

  & to solve in terms of "y":

2y / 2 = (x-1)/2 ;

to get:

y = (x-1)/2 ;

or; write as:  y = (x/2) - (1/2);

Now, rewrite; by replacing the "y" with "f⁻¹(x) "; as follows (to indicate that this is the "inverse function"):

f⁻¹(x) = (x-1)/2 ;  or, write as:

f⁻¹(x) = (x/2) - (1/2) .

Hope this is helpful to you!

 Best wishes!

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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