f(x) = 5x - 12
Let's say...
y = 5x - 12
Now solve this equation for x .
y + 12 = 5x
(y + 12) / 5 = x
To get the inverse function, swap x and y . Instead of " y " I put " f-1(x) "
f-1(x) = (x + 12) / 5
And we want to find what x value makes...
f-1(x) = f(x + 1)
That is...
(x + 12) / 5 = 5(x + 1) - 12
Multiply both sides by 5 .
x + 12 = 25(x + 1) - 60
x + 12 = 25x + 25 - 60
Subtract 25x from both sides and subtract 12 from both sides.
x - 25x = -12 + 25 - 60
-24x = -47
x = 47/24
f(x) = 5x - 12
Let's say...
y = 5x - 12
Now solve this equation for x .
y + 12 = 5x
(y + 12) / 5 = x
To get the inverse function, swap x and y . Instead of " y " I put " f-1(x) "
f-1(x) = (x + 12) / 5
And we want to find what x value makes...
f-1(x) = f(x + 1)
That is...
(x + 12) / 5 = 5(x + 1) - 12
Multiply both sides by 5 .
x + 12 = 25(x + 1) - 60
x + 12 = 25x + 25 - 60
Subtract 25x from both sides and subtract 12 from both sides.
x - 25x = -12 + 25 - 60
-24x = -47
x = 47/24