f the point (–2, 4) is on the graph of y = f(x), what point is on the graph of y = f^–1(x + 1)?

Question

A) (3, –2)

B) (5, –2)

C) (1, –4)

D) (4, –3)

Answer 1

C) (3,-2)

(-2,4) is on f(x)

so (4,-2) is on the inverse f^-1(x), just switch x and y coordinates, (x,y) to (y,x)

then subtract 1 to the x coordinate for f^-1(x+1)

to get (4-1,-2) = (3,-2)

try a simple function, y=x+1 = f(x)

then the inverse is x=y+1 or y = x-1

(1,2) is on f(x), and (2,1) is on the inverse

f^-1(x+1) shifts y=x-1 to the left by 1 unit, to y = x+1-1 = y=x

(2,1) becomes (2-1,1)= (1,1)

or f(x)=y=-2x has the point (-2,4)

the inverse f^-1(x) is x=-2y or y=-x/2 which has the point (4,-2) as -2=-4/2

the inverse shifted left by 1 unit is f^-1(x+1) =y = -(x+1)/2 which includes the point (3,-2) as -2=-(3+1)/2