Functions
The function f is defined by f(x) = x^2 + 5.
Do you agree that f(3) = 14? True or False?
True
If f(x) = 7x - 5, determine f^-1(x)
f^-1(x) = (x+5)/7
If f(x) = 9 + x and g (x) = x^3, calculate fg(x)
fg(x) = 9 + x^3
If f(x) = 2x + 1 and g (x) = x^2, calculate (fg)^-1(x)
(fg)^1(x) = sqrt((x-1)/2)
If y is directly proportional to x, and y = 10 when x = 2.5, determine the value of k
k = 4
Evaluate x, if g(x)=26 and g(x)=3(x-1) + 2
x = 9
Given h(x) = (5x-1)/(3x+1), write an expression for h^-1(x)
h^-1(x) = (x+1)/(5-2x)
If f(x) = 3x - 2 and g (x) = 2x + 5, calculate fg(3)
fg(3) = 31
If f(x) = 2x + 1 and g (x) = 3x-2, calculate (fg)^1(x)
(fg)^1(x) = (x + 3)/6
If y is directly proportional to x, and y = 10 when x = 15, determine the value of y when x = 21
y = 14
If f(x)= (1/2)(4x-1), calculate the value of f(-2)
f(-2) = -4.5
The function g is defined as g(x) = x^3. Determine an expression for g^-1(x)
g^-1(x) = x^(1/3) or the cube root of x
If g(x) = (2x + 1)/(x - 1) and h(x) = (4x+3)/(x - 2), calculate gh(-2)
gh(-2) = 14
If f(x) = x - 3 and g (x) = 4x + 1, calculate f^-1g^-1(-3)
f^-1g^-1(-3) = 2
If y is inversely proportional to x^2, and y = 5 when x = 4, determine the positive value of x when y =20
x = 2
Given the function f(x) = 3x^2 + 2x - 1. Evaluate f(-1)
f(-1) = 0
The function g(x) = (4x+1)/(3x-2), find the inverse of g(x) and determine the value of g^-1(1)
g^-1(x) = (2x+1)/(3x-4)
g^-1(1) = -3
If f(x) = 2x + 1 and g(x) = (3x - 1)/(2x + 1), calculate gf(1/2)
gf(1/2) = 1
If f(x) = 2x + 1 and h(x) = 4x, calculate fh^-1(x)
fh^-1(x) = (x - 1)/8
If y is directly proportional to x, and y = 36 when x = 12, determine the value of y when x = 24
y = 72
Given g(x) = (3x-1)/(x+2) and h(x) = (7x+1)/(5x-2). Find g(3) and h(2)
g(3) = 8/5
h(2) = 15/8
If h(x) = (3x+5)/(x+5) and its inverse is calculated to be h^1(x) = (5x-5)/(3-x).
Calculate h(x) = 2
Also, state the real value of x which cannot be in the domain of h(x)
When h(x)=2, x = 5
The real value which cannot be in the domain of h(x) is x cannot be equal to -5
If f(x) = x^3, h(x) = 2x + 1 and g(x) = x - 3, calculate fgh(x)
fgh(x) = (2x - 2)^3
If f(x) = 3x, h(x) = x + 1 and g(x) = 4x - 3, calculate (fgh)^-1(x)
(fgh)^-1(x) = (x - 3)/12
If y is inversely proportional to the cube of x, and y = 8 when x = 3, determine the value of y when x = 6
k = 216
y = 1