+62 if $$f(x)=2x-7,g(x)=\sqrt{3x-2},x\geq 2$$ then
$$(f^{-1}o g^{-1})(5)=?$$
$$(g^{-1}o f^{-1})(-3)=?$$
+129852 Let's find the inverse of both functions
y = 2x - 7 add 7 to both sides y= √(3x - 2) square both sides
y + 7 = 2x divide both sides by 2 y^2 = 3x - 2 add 2 to both sides
(y + 7) / 2 = x exchange x with y y^2 + 2 = 3x divide both sides by 3
(x + 7) / 2 = y = f-1(x) ( y^2 + 2) / 3 = x exchange x and y
(x^2 + 2 ) / 3 = y = g-1(x)
And g-1(5) = (25 + 2) / 3 = 9
So f-1 (g-1(5)) = f-1 (9) = (9 + 7) / 2 = 16 / 2 = 8
And f-1 (-3) = ( -3 + 7) / 2 = 4 / 2 = 2
So g-1 (f-1(-3)) = g-1 (2) = (2^2 + 2 ) / 3 = (6) / 3 = 2
+129852 Let's find the inverse of both functions
y = 2x - 7 add 7 to both sides y= √(3x - 2) square both sides
y + 7 = 2x divide both sides by 2 y^2 = 3x - 2 add 2 to both sides
(y + 7) / 2 = x exchange x with y y^2 + 2 = 3x divide both sides by 3
(x + 7) / 2 = y = f-1(x) ( y^2 + 2) / 3 = x exchange x and y
(x^2 + 2 ) / 3 = y = g-1(x)
And g-1(5) = (25 + 2) / 3 = 9
So f-1 (g-1(5)) = f-1 (9) = (9 + 7) / 2 = 16 / 2 = 8
And f-1 (-3) = ( -3 + 7) / 2 = 4 / 2 = 2
So g-1 (f-1(-3)) = g-1 (2) = (2^2 + 2 ) / 3 = (6) / 3 = 2
