Question

Explain how to find the inverse of f(x) = (x-1)/4

Answer 1

You can generally solve for inverse of a function using the following steps:
1) Replace f(x) with y
2) Switch x's and y's
3) Solve for y
4) Replace 'y' with 'f^-1(x)'

Answer 2

y=x*4 +1
y=4x+1

Answer 3

you see from PEMDAS which tells your the order of operations to perform, has to be undone to get what the input was for a given output.

Answer 4

Is this right: ?

if g(x) is the inverse of f(x), then, by definition, f(g(x)) = x

f(x) = (x-1)/4
f(g(x)) = (g(x)-1)/4 = x
g(x) = 4x + 1

But, since g(x) is the inverse of f(x),
f^-1(x) = g(x) = 4x+1

Answer 5

so if you look at your expression
f(x)=(x-1)/4
the first thing you did was -1, then we /4
so to undo this
we look at the last operation /4, that becomes *4
then -1 becomes +1
f-1(x) = 4*x + 1

Answer 6

yeah you did it right

Answer 7

Thank you!

Answer 8

I like how you use f(g(x)) it's very clean