Domain
What is the domain of f(x)=(x+2)2? Use restricted domain if it needs to be restricted to find inverse.
[-2,infinity)
What is the range of f(x)=(x+2)2?
[0,infinity)
What is the inverse of f(x)=(x+2)2?
f-1(x)= x1/2-2
Verify algebraically whether the functions are inverses of each other:
f(x)=5x-6
g(x)=-1/5(x-6)
no, they are not inverses
Simplify
x-1/2(2x1/2-x-1/2)
(2x-1)/x or 2 - 1/x
What is the domain of g(x) = (2-x)/(3+x)? Use restricted domain if needs to be restricted to find inverse.
x cannot be -3
What is the range of g(x) = (2-x)/(3+x)?
y cannot be -1
What is the inverse of g(x) = (2-x)/(3+x)?
g-1(x)=(2-3x)/(x+1)
Verify algebraically whether the functions are inverses of each other:
f(x) = (x+3)1/2
g(x) = x2+3
No, they aren't inverses.
Simplify
x1/4(x1/3) / (x1/6)
x5/12
What is the domain of f(x)=ex-4? Use restricted domain if needs to be restricted to find inverse.
all reals
What is the range of f(x)=ex-4?
(0,infinity)
What is the inverse of f(x)=ex-4?
f-1(x)=lnx+4
Verify algebraically whether the functions are inverses of each other:
f(x)= -1/3(x+2)
g(x)=2-3x
No, they aren't inverses.
Simplify
(-3n-3)2/(-9n-4)
-1/n2
What is the domain of f(x)=-2/3[absval(x-2)]+4? Use restricted domain if needs to be restricted to find inverse.
x is greater than or equal to two
What is the range of f(x)=-2/3[absval(x-2)]+4
(neg infinity, 4]
What is the inverse of f(x)=-2/3[absval(x-2)]+4
f-1(x)=-(3/2)x+8
Verify algebraically whether the functions are inverses of each other:
f(x)=1/(x-4)
g(x)=(4x+1)/x
Yes, they are inverses.
Solve
8x=27 (49)
x= 25/3
What is the domain of f(x)= log(2x+5)?
x is greater than 5/2
What is the range of f(x)= (x+4)3-3?
all reals
What is the inverse of f(x)= (x+4)3-3?
f-1(x)=(x+3)1/3-4
Verify algebraically whether the functions are inverses of each other:
f(x)= (2x)/(x+3)
g(x)= (3x)/(2-x)
Yes, they are inverses
Solve
9x(37x-1)=33+x
x=1/2