Transformations Review Math 30-1

Question

The graph of y=f(x) is reflected in the line y=x and then translated right 4 and down 1 resulting in another function g(x). Write the equation of g(x) in terms of f^-1(x)

Answer 1

right 4: f(x+4)

down 1 f(x+4)-1

g(x) = f(x+4)-1

then find g^-1(x)

switch x and y and solve for new y

old y = g(x)

x = f(y+4)-1

solve for new y

x+1 = f(y+4)

y+4 = f^-1(x+1)

y =g^-1(x) = f^-1(x+1) -4

try a specific example to see better what's going on, and to check your more general answer

y=f^-1(x) = x^2, an upward opening parabola

shift it left by 4: y=(x+4)^2

shift down by 1

y = (x+4)^2 -1

switch x and y

x =(y-1)^2 -4

solve for the new y