Difficult Graph Problem

Question

Find the inverse of the function. (Enter the domain using interval notation.)

f(x) = (x + 9)²,   x ≥ −9

How would you put that in a graph?

Answer 1

y = (x+9)^2 has an inverse function found by switching x and y

x=(y+9)^2

solve for y

take square roots of both sides

y+9 = + and - sqrx

subtract 9 from both sides

y= -9 + or - sqrx

f^-1(x) = -9 + or - sqr(x)

the original function was a parabola with vertex (-9,0) opening upwards with line of symmetry x=-9

this inverse function is a parabola, with vertex at (0,-9) opening to the right

the two functions are inverses of each other, mirror images

You can get one graphically by rotating the other around the 45 degree diagonal line

But the domain of the original function was x>-9, so it's only the right half of the parabola

with x>-9 and y>0

Same with the inverse function, it's also just half of a parabola, with y>-9

and x>0

the x and y get switched for the inverse

to get only the top half of the parabola for the inverse function

the equation is y=-9 + sqr(x)

and not + or - sqr(x)

For interval notation

the domain of the original function is (-9, infinity)

For the inverse

the domain is (0, infinity)

use a figure 8 on it's side for infinity

use parentheses, not brackets, as the domains do not include

either end point. You never reach infinity, and the problems states x>-9, not = or >

and when you graph the half parabola, leave a small circle at (-9,0) for the first fuction

and a small circle at (0,-9) for the inverse to indicate the graph does not include those points