find the inverse of f(x)=-4+7/2 x

Question

find the inverse of f(x)=-4+7/2 x

Answer 1

Find the inverse of  f(x) = -4 + (7/2)x

 

y = -4 + (7/2)x           change f(x) to y

 

x = -4 + (7/2)y          switch the x and y variables 

 

Solve equation for y

 

x + 4 = (7/2)y

 

2 ( x + 4) = y

     7

 

y = f^-1 (x) = 2 (x + 4 )

                       7

 

Answer 2

y = f(x) ; we desire the inverse x = g(y) so that f[g(y)]=y and g[f(x)] = x

 

y = -4 + 7/2 x ⇒ 2(y + 4) = 7 x ⇔ x = 2/7 (y + 4 )

 

g(x) = 2/7 x + 8/7 the inverse of f(x)

 

 

Answer 3

f(x) = -4 +7x/2

x = -4 + 7f^-1(x)/2          rewrite as inverse

x + 4 = 7f^-1(x)/2           add 4 to both sides

2(x + 4) = 7f^-1(x)          multiply both sides by 2

2(x + 4)/7 = f^-1(x)         divide both sides by 7