f(x)=sqrtx+6

f(x)=sqrtx+6 --> y = sqrtx + 6 --> Solve for x in terms of y -->

y - 6 = sqrtx -->

(y - 6)^2 = x --> Switch "x" and "y" --> y = (x - 6)^2.

f(x)=sqrtx-3 --> y = sqrtx - 3 --> Solve for x in terms of y -->

y + 3 = sqrtx -->

(y + 3)^2 = x --> Switch "x" and "y" --> y = (x + 3)^2.

you are a LIFESAVER

these are also wrong

If the first one is supposed to be...

y = √(x + 6)   then square both sides

y² = x + 6    subtract 6 from both sides

y² - 6  = x      now, "switch" x and y

x² - 6  = y     

y = x² - 6    now, for "y,"   write   f ^-1(x)

f ^-1(x) = x² - 6      ......and that's the inverse......

Nataszaa....I don't like to sound critical, but you need to use parentheses and brackets to specify WHAT you mean!!  Aziz didn't work these problems "incorrectly,"   ....he actually worked with what was represented....

y = √(x) + 6   ...which is what you have and what Aziz worked with......is different from  y = √(x + 6) ......which is what I "interpreted."

Nataszaa you need to learn to use brackets.  

Your questions cannot be answered the way you want if you ask the wrong question!