Midterm Exam Review

Inverse Functions

100

f(x)=x²-3x+4

g(x)=5x+2

h(x)=6x

a) f(g(h(-1)=

872

200

Find the inverse:

f(x)=(2x+4)^1/3

f^-1(x)=(x³-4)/2

300

Find the inverse:

f(x)=(x-2)/4

f^-1(x)= 4x+2

400

Are the following two functions inverses? Verify using composite functions.

f(x)= (x⁵+2)/7        g(x)=(7x-2)^1/5

yes

f(g(x))=x

500

State 3 characteristics of inverse functions.

reflective about y=x

f(g(x))=x

(x,y)-(y,x)

Logarithmic Functions

100

Write the logarithm as a single logarithm.

logx+1/2(log y)-2 logz

log (xy^1/2)/z²

200

Evaluate:

a) log₁₆4

b)log_1/39

a) 1/2

b) -2

300

Find the inverse:

y=log(x+3)-4

f^-1(x)=10^x+3-4

400

Graph:

y= log (x+2) -1

State the domain and range.

domain(-2, infinite)

range(-inf, +inf)

500

Lynn bought a car in 2022 for $24,500.  It depreciates at a rate of 4.2% a year.  Write a function to model this and what will the car be worth in 2027?

f(x)= 24,500(.958)^x

x= yrs since 2022

y= value of the car in $

$19,769.41

Functions

100

Simplify:

4(440x¹¹y¹⁵z⁵)^1/3

2x³y⁵z¹(55x²z²)^1/3

200

Solve:

2(3x-1)^1/2+3=11

17/3

300

Graph and state the domain and range.

f(x)=2|x-1|-4

d: (-inf, inf)

r:[-4, inf)

400

Graph:

f(x)=(2x+1)/(x+3)

D:

R:

D: all real number x not equal to -3

R: all real number y not equal to 2

500

Solve

3|x+5| -2= 6

-7/3, -23/3

Polynomials

100

(2x²-x+3)²

4x⁴-4x³+13x²-6x+9

200

Factor:

a)32x²-2=0

b) 6x²+7x-3=0

c) 8x³-125=0

a) 2(4x-1)(4x+1)

b) (3x-1)(2x+3)

c) (2x-5)(4x²+10x+25)

300

(3x²+10x+8)/(x+2)

3x+4

400

Find all the roots and tell if the function is odd,even or neither:

f(x)=x⁴-2x³+10x²-18x+9

1,1,3i,-3i

neither

500

Solve:

2x³+7x²-28x+12=0

2,-6,1/2

Solving Functions

100

Solve 

5^3x=25^x-1

x=-2

200

log₈(x-5)=2/3

x=9

300

Solve

10^2x+3=8

x=.349

400

Solve:

(6x/x+4)+4=(2x+2/(x-1))

2, -3/2

500

Solve:

(3x+2)^1/2-2x^1/2=0

2