Equations, Inequalities, and Systems
Solve the equation. Be sure to check for any extraneous solutions. (See doc)
x = 62
State the domain and range of the following function. (See doc)
D: x ≥ -2
R: y ≥ -1
Given the table of values, is f-1(x) a function? Why or why not? (See doc)
No; the domain value of 2 would have a range value of both 1 and 3.
Find the inverse of the function.
f(x) = -0.5x + 10
f-1(x) = -2x + 20
Solve the equation. Be sure to check for any extraneous solutions. (See doc)
x = 36, -36
f(g(-1)) = 4
Which option has an inverse that is a function? (See doc)
The set of ordered pairs.
Find the inverse of the function.
f(x) = -x3 - 9
f-1(x) = cube root(-x - 9)
Solve the inequality. (See doc)
x > 9
Given the functions h(x) and j(x), find the domain of (h/j)(x). (See doc)
[-3, -1) U (-1, infinity)
Given that f(x) is a linear function with a y-intercept of -2 and slope of 2, write an equation for f-1(x).
y = (x/2) + 1
Find the inverse of the function. Be sure to state any domain restrictions. (See doc)
f-1(x) = (1/9)(x - 5)2 , x ≥ 5
Solve the inequality. (See doc)
8 ≤ x < 152
Given a(x) and b(x), find the domain of a(b(x)). (See doc)
x ≥ 1/2
Graph the inverse of the blue function. (See doc)
See doc.
Determine whether the functions f(x) and g(x) are inverse functions.
f(x) = -2x + 6
g(x) = -0.5x + 3
Yes; both f(g(x)) and g(f(x)) are equal to x.
Solve the nonlinear system.
x2 + y2 = 1
y = 0.5x2 - 1
(0, -1)
Given m(x) and n(x), find m(n-1(-3)). (See doc)
m(n-1(-3)) = 6
Given that the function in black is f(x) and the function in blue is g(x), find f(g-1(-3)). (See doc)
f(g-1(-3)) = 2
Determine whether the functions f(x) and g(x) are inverse functions.
f(x) = 4(x - 11)2
g(x) = 0.25(x + 11)2
No; it is not true that both f(g(x)) and g(f(x)) are equal to x.