Inverse of functions
Find the inverse of
f(x) = x + 3
Algebra: Is this a function: {(1, 2), (2, 3), (2, 4)}
No
Find the slope: 2(3x - y) = -10
3
Given
f(x) = 4x +3
Evaluate f(3)
f(3) = 4(3) + 3
f(3) = 15
Model the following function
A number increases by three each term.
f(n) = (n-1)3
Find the inverse of
f(x) = 3x + 15
Given
f(x) = sqrt(x+5)
What is the domain and range?
(Desmos needed)
Domain: [-5, infinity)
Range: [-5, infinity)
What is the slope of the following equation:
2x + 2y = 8
slope = -1
Given
f(x) = 3x +5
Find f(x+2)
f(x+2) = 3x + 11
Model the following function:
$4,000 invested grows by 3% each year. How much is the investment worth after 15 years?
f(x)=4000(1+.03)^15
$6231.86
Find the inverse of
f(x) = (-5x/3)
Solve for a in
ax + b = c
a = (c - b)/x
- subtract b, divide by a
Solve: (3 - 3x)/7 = 6
x = -13
Given
f(x) = 3x
g(x) = 2x + 3
Find g(f(3))
f(3) = 3(3)
f(3) = 9
g(9) = 3(9)
g(f(3)) = 27
Model the following:
A term, 7, increases by three each next term.
f(n) = 7+(n-1)3
Find the inverse of
f(x) = x^2
f^-1(x)= sqrt(x)
Solve for y
3x + 11y = 4y - 4x^2
y = (-4x^2 - 3x)/7
Given
f(x) = 4x + 5
g(x) = 3x^2
Find (f*g)(x)
(4x+5)(3x^2) =
(f*g)(x) = 12x^3 + 15x^2
24, 72, 216
r = 3
k = 8
Find the inverse of
f(x) = sqrt(5x+3)
f^-1(x)= (x^2/5) - (3/5)
Given
f(x) = x^2
What is the domain and range?
Domain: All real numbers (-infinity, infinity)
Range: All real numbers (-infinity, infinity)
What's the slope of the line passing through (3,9) (5,4)
slope: -5/2
f(x) = 15x - 11
g(x) = 3x^2
(f o g)(x+2)
g(x+2) = 3(x+2)^2
g(x+2) = 3x^2 + 12x + 12
f(3x^2 + 12x + 12) = 15(3x^2 + 12x + 12) - 11
f(3x^2 + 12x + 12) = 45x^2 + 180x + 169
3, 9, 27, 81
Identify if it is Geometric or Arithmetic
Geometric sequence
f(n) = 3(3)^n-1