It takes you seconds to walk from the first (ground) floor of a building to the third floor. How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)? It will take
nothing seconds to walk from the first floor to the sixth floor.

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Ответ:

shelovejaylocs

30.05.2022

Mathematics

The inverse of the function is $g(x)=\frac{5}{2}x+10$ .

Step-by-step explanation:

The given function is

$f(x)=\frac{2}{5}x-4$

$y=\frac{2}{5}x-4$

Interchange the variable x and y.

$x=\frac{2}{5}y-4$

Now find the value of y in terms of x,

$x+4=\frac{2}{5}y$

5(x+4)=2y

5x+20=2y

Divide both sides by 2.

$y=\frac{5}{2}x+10$

Put y=g(x)

$g(x)=\frac{5}{2}x+10$

Therefore the inverse of the function is $g(x)=\frac{5}{2}x+10$ .

If two function f and g are inverse of each other then $(f\circ g)(x)=x$ .

$(f\circ g)(x)=f(g(x))$

$(f\circ g)(x)=f(\frac{5}{2}x+10)$

$(f\circ g)(x)=\frac{2}{5}(\frac{5}{2}x+10)-4$

$(f\circ g)(x)=x+4-4$

$(f\circ g)(x)=x$

Therefore f(x) and g(x) are inverse of each other.

Graph of both functions are mirror image of each other across the line y=x, therefore functions are inverses of each other.

Consider the function f(x)= 2/5x - 4 a. find the inverse of and name it . show and explain your work

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