Question

Define g: R→R by the rule g(x)=4x-5 for all real number x. Find g-1(y)

Answer 1

Since it is linear, we can just "reverse" our steps.

e.g. for g(x) , for any x, the first thing we do is multiply it by 4 and then subtract 5

now doing this backwards, start with an x, add 5, then divide that be 4

so g^-1 (x) = (x+5)/4

standard method:
step1 : interchange x and y variables
y = 4x-5 -----> x = 4y-5
step2: solve this inverse equation for y
4y - 5 = x
4y = x+5
y = (x+5)/4 , same as above