Operation on Function
f(x) = x ; g(x) = x3
What is f(x) + g(x)?
x + x3
Solve for x:
3x - 25 = 2x + 5
x = 30
if f(x) = x3 + x2
What is f(2)?
12
for x - 3 > 0
Determine if x = -1 is a Solution or Not a Solution?
Not a Solution
A relation in which the domain corresponds to a unique range.
Function
Given f(x) = x + 2 and g(x) = x2−4
Solve for (f + g)(x)
x2 + x - 2
178x2 - 5x = 90x
95/178
f(x) = (x + 5)/(2x - 5)
Find f(4)
3
What are the critical values of:
(x + 8)/(2 - x) > 0
Indicate proper ( or [
(-8, 2)
It is the set of all y-coordinates.
Range
f(x) = x2 - 12 and g(x) = x2 + 12
Solve for (f * g)(x)
x4 - 144
What is the least common multiple of x2-16 and x2+4x-32?
(x + 4)(x – 4)(x + 8)
f(x) = 10x/(-x - 5)
Find f(9)
-45/7
Solve for the solutions of x for:
(x - 1)/(x + 2) < 0
x ∈ R | -2 < x < 1
It is a special kind of relation where each element in the domain is related to only on value in the range by some rule. It is also a set of ordered pairs (x,y) such that no two ordered pairs have the same x-value but different y-values.
Function
Given f(x) = x + 2 and g(x) = x2 + 5x + 6
Solve for f / g
1/(x + 3)
60/(w-5) - 18/w = 40/w
-145
f(x) = -3/(2x - 8)
Find f(√ 3)
(6√ 3 + 24)/52
Solve for the solutions of x for:
-2/(x - 10) < 0
x ∈ R | x > 10
A function define by multiple sub-functions, where each sub-function applies to a certain interval of main function's domain.
Piecewise Function
f(n) = 3n + 4 and g(n) = n3 − 5n
Find f(n/2) - g(n/2)
(32 + 23n − n3)/8
3/(x2 - x - 12) + 2/(x2 + x - 6) = 4/(x2 - 6x + 8)
26
for f(x) = x2 + 9x +18
provide the ranges as the set of domains are (1,2,3) respectively.
28, 40, 52
Solve for the solutions of x for:
2/(p - 1) ≥ 3/4
x ∈ R | 1 < p ≤ 11/3
Switching of the variables x and y into the function.
Inverse Function