For this case we must find the inverse of the following function:
[tex]f (x) = 4x + 7[/tex]
For it:
Replace f (x) with y:
[tex]y = 4x + 7[/tex]
We exchange the variables:
[tex]x = 4y + 7[/tex]
We solve for y:
We subtract 7 on both sides of the equation:
[tex]x-7 = 4y[/tex]
We divide between 4 on both sides of the equation:
[tex]y = \frac {x} {4} - \frac {7} {4}[/tex]
Finally, we change y by[tex]f ^ {- 1} (x)[/tex]:
[tex]f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}[/tex]
