Answer:
[tex]\displaystyle {f}^{ - 1}(x) = \frac{1}{4} (x - 18x + 85)[/tex]
Step-by-step explanation:
we would like to find the inverse of the following function:
[tex] \displaystyle f(x) = 9 + \sqrt{4x - 4} [/tex]
to do so substitute y for f(x):
[tex] \displaystyle y= 9 + \sqrt{4x - 4} [/tex]
interchange variables:
[tex] \displaystyle x= 9 + \sqrt{4y - 4} [/tex]
cancel 9 from both sides:
[tex] \displaystyle \sqrt{4y - 4} = x - 9[/tex]
square both sides:
[tex] \displaystyle 4y - 4= x - 18x + 81[/tex]
add 4 in both sides:
[tex]\displaystyle 4y = x - 18x + 85[/tex]
divide both sides by 4:
[tex]\displaystyle y = \frac{1}{4} (x - 18x + 85)[/tex]
substitute back:
[tex]\displaystyle {f}^{ - 1}(x) = \frac{1}{4} (x - 18x + 85)[/tex]
and we're done!
