Practice Test Flashcards
Find fog and gof of
f(x)=x+1/x-1
g(x)= 1/x-2
fog: x-1/x-2
gof: x-1/3/x
f(x)= -3^x+1 + 4
Find f^-1
= f-1(x)=ln(4-x)-1
Find exact value
log2(8)
=3
Find exact value
ln(e sq. of x)
= square root of x
Find exact value
2log2(0.4)
= 0.4
Solve 8^6x+3 =4
x = -17/18
Solve logx(64)=3
x=4
Solve log6(x+3)+log6(x+4)=1
x= -1
Explain why a degree 5 polynomial must have a range of negative infinity to infinity
The end behavior of all degree five polynomial look like an S or backwards S
Explain why a degree 10 polynomial cannot have exactly 7 real roots (including repeated roots)
Having 7 real roots implies 3 complex roots, which violates the conjugate pair theorem
What is the max turning points on the equation f(x)= (2x+1)(x-3)^2
Max is 2 because degree is 3
What is the end behavior of the equation f(x)= (2x+1)(x-3)^2
as x approaches infinity, f(x) approaches infinity. as x approaches - infinity, (x) approaches - infinity
Find roots, multiplicity, and local behavior
f(x)= (2x+1)(x-3)^2
roots: -1/2 and 3
Multiplicity: 1 and 2
Local behavior: =(pos)(2x-1) and = 5(x-3)^2
Evaluate table one
What is (fog)(2)?
f(g(3)) = 1
Evaluate table one
What is (gof)(2)?
g(f(5))=4
Evaluate table one
What is (fog)(1)?
f(f(4))=0
Evaluate table one
What is (gog)(5)?
g(g(4))=0
Evaluate table one
Is f one-to-one? is g?
F is not one to one because f(0) = f(5) = 3
G is not one to one because g(1) = g(4) = 0
What is the domain of fog
F(x)=x+1/x-1
g(x)= 1/x-2
fog is not 2 or 3
What is the domain of gof
F(x)=x+1/x-1
g(x)= 1/x-2
gof is not 1 or 3
find f-1 given f(x)=3(x-1)^5 +7
5 square root of x-7/3 + 1
