f(x) question

Question

Given the function f(x)=5x+4 , find its inverse

 

A. f ^-1 (x)=(x−5)/4 

B. f ^-1 (x)=x/5 −4 

C. f ^-1 (x)=(x−4)/5 

D. f ^-1 (x)=x/4 −5

 

please explain so I can understand thanks

Answer 1

To find the inverse, what we essentially do is isolate the essentially y-variable and treat that as the new equation.

y = 5x + 4

y - 4 = 5x

^{(y - 4)}/₅ = x or

¹/₅ y - ⁴/₅ = x if you want to distribute the ¹/₅.

And now we switch the positions of the variables (also change y to f^-1(x)):

f^-1(x) = ^{(x - 4)}/₅