The graph above is a transformation of the function Wist an

The graph above is a transformation of the function Wist an equation for the function graphed above Write an equation for the function graphed above Preview 011) g(z) = -sqrt(x+2)-3 t1/1] Points possible: 1 This is attempt 3 of 3. Score on last attempt: 0. Score in gradebook: 0 1i Submit 21 (0/1) 222 1/1 023 (1/1) Q24 1/1 025 111 9261/1 Q2711/11

Solution

f(x) = x

first tranformation : It is mirror image of x about y - axis

==> f(x) = -x

second tranformation : It is moved 2 units to the left

==> f(x) = -(x +2) = (-2 - x)

third tranformation : It is moved 3 units downwards

==> f(x) = (-2 - x) - 3

==> final function is f(x) = -3 + (-2 - x)

2) f(x) = (x + 4)/(6x - 6)

let f(x) = y ==> y = f^-1(x)

==> y = (x + 4)/(6x - 6)

==> y(6x - 6) = x +4

==> 6xy - 6y = x + 4

==> 6xy -x = 6y + 4

==> x(6y - 1) = (6y + 4)

==> x = (6y + 4)/(6y - 1)

==> f ^-1(y) = (6y + 4)/(6y - 1)

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

==> f ^-1(x) = 2(3x + 2)/(6x - 1)