Inverse Functions
When finding the inverse of a function, what is the first thing you should do?
Swap the x and y
Determine the domain and range of f(x).
f(x)=sqrt x
D:[0,infty), R: [0,infty)
What is the parent sqare-root function?
f(x)=sqrtx
Rewrite the expression using rational exponents
sqrt x
x^{1/2}
What must you do after solving a radical equation?
Check for extraneous solutions.
Find the inverse of the function.
f(x)=x+7
f^{-1}(x)=x-7
Evaluate the expression
sqrt 49
7
f(x)=sqrtx, g(x)=sqrt{x-4}
Describe the transformation between f(x) and g(x)
Horizontal translation 4 units right
Rewrite using rational exponents
root(3)(x)
x^{1/3}
Solve
sqrtx=5
x = 25
Find the inverse of the function.
f(x)=3x-5
f^{-1}(x)=\frac{x+5}{3}
Evaluate the expression
root(3)(-64)
-4
Describe the transformation
f(x)=sqrtx+3
Vertical translation 3 units up
Simplify
sqrt 50
5sqrt2
Solve
sqrt{x+4}=6
x = 32
Find the inverse of the function.
f(x)=x^3
f^{-1}(x)=root(3)(x)
Find the domain and range of the function.
f(x)=sqrt{x-5}
D: [5,infty), R: [0,infty)
Describe the transformation
f(x)=2sqrtx
Vertical dilation by factor of 2
Simplify
root(3)(54)
3root(3)(2)
Solve
sqrtx+3=7
x = 16
Verify that the following functions are inverses.
f(x)=\frac{4x-2}{4}, g(x)=\frac{4x+2}{4}
Yes, f(x) and g(x) are inverses of each other.
Find f(27)
f(x)=root(3)(x)
3
Describe the transformations:
f(x)=5sqrt{x-2}
1) Horizontal translation 2 units right
2) Vertical dilation by 5
Simplify
frac{5}{sqrt3}
Or 5/ V3
frac{5sqrt3}{3}
5 V3/3
Solve
sqrtx-x=-6
x = 9
The function f(x) contains the point (-3,8). What point must lie on the inverse function of f(x)?
(8,-3)
Find the domain and range of f(x).
f(x)=sqrt{2x+3}-4
D:[-3/2,infty) or [-1.5,infty), R: [-4,infty)
Let g(x) be a transformation of f(x) with a horizontal translation 6 units left and a vertical translation 5 units down. Find g(x).
f(x)=sqrtx
g(x)sqrt{x+6}-5
Simplify
root(3)(8x) + root(3)(27x) + root(3)(x)
6 root(3)(x)
Solve
sqrt{2x+3}=x
x=3