Home > Precalculus > Introduction to Twelve Basic Functions

How do you find the inverse of #f(x) = 6x - 4#?

Answer 1

Chloe Alexander

#f^(-1)(x)=(x+4)/6#

First, switch the positions of #x# and #y#. #y=6x-4# Inverse: #x=6y-4#.

Next, isolate #y#. #x=6y-4# #x+4=6y# #(1/6)(x+4)=(1/6)6y# #color(red)(y=(x+4)/6)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Anna Allen

To find the inverse of the function ( f(x) = 6x - 4 ), follow these steps:

Replace ( f(x) ) with ( y ).
Swap the roles of ( x ) and ( y ), so the equation becomes ( x = 6y - 4 ).
Solve this equation for ( y ) to find the inverse function ( f^{-1}(x) ).
After solving for ( y ), replace ( y ) with ( f^{-1}(x) ).

Now, let's solve the equation ( x = 6y - 4 ) for ( y ):

[ x = 6y - 4 ] [ x + 4 = 6y ] [ \frac{x + 4}{6} = y ]

So, the inverse function ( f^{-1}(x) ) is:

[ f^{-1}(x) = \frac{x + 4}{6} ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.