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!

b

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."