Function Operations
Find (f+g)(x) when,
f(x) = 3x^2 - 4
g(x) = x^2 - 8x + 4
(f+g)(x)=4x^2 - 8x
Given the following functions, find g(h(x)).
f(x) = x^2 - 2x + 3
g(x) = x - 4
h(x) = 2x^2 - 5x - 6
g(h(x)) = 2x^2 - 5x - 10
Find the inverse of
f(x) = x + 2
f^-1(x) = x - 2
Determine if the two functions are inverses of each other.
f(x) = 2x + 3
g(x) = 2x - 3
No
From Latin for "twice" & "cut", it means to divide a line or figure into 2 equal parts
bisect
Find (f-g)(x) when,
f(x) = 3x^2 - 4
g(x) = x^2 - 8x + 4
(f-g)(x)=2x^2 + 8x - 8
Given the following functions, find g(h(0)).
f(x) = x^2 - 2x + 3
g(x) = x - 4
h(x) = 2x^2 - 5x - 6
g(h(0)) = -10
Find the inverse of
f(x) = (x-4) / 3
f^-1(x) = 3x + 4
Determine if the two functions are inverses of each other.
f(x) = 4x + 6
g(x) = (x - 6) / 4
Yes
"Like fractions" have the same this, making it easy to add & subtract them
denominators
Find (f x g)(x) when,
f(x) = 3x^2 - 4
g(x) = x^2 - 8x + 4
(f x g)(x)= 3x^4 - 24x^3 + 8x^2 +32x - 16
Given the following functions, find f(g(x)).
f(x) = x^2 - 2x + 3
g(x) = x - 4
h(x) = 2x^2 - 5x - 6
f(g(x)) = x^2 - 10x + 27
Find the inverse of
f(x) = x^2 + 3
f^-1(x) = +-sqrt(x - 3)
Determine if the two functions are inverses of each other.
f(x) = - 1/3x + 3
g(x) = -3x + 9
Yes
In a Tom Lehrer song, a movie called "The Eternal Triangle" stars Ingrid Bergman as this longest side of a right triangle
a hypotenuse
If (f+g)(x) = x^2 -2x + 3, and f(x) = x^2 +1, then what is g(x)?
g(x) = -2x + 2
Given the following functions, find f(g(2)).
f(x) = x^2 - 2x + 3
g(x) = x - 4
h(x) = 2x^2 - 5x - 6
f(g(2)) = 11
Find the inverse of
f(x) = sqrt(x-5) - 7
f^-1(x) = (x+7)^2 + 5
Determine if the two functions are inverses of each other.
f(x) = (x + 6)^2
g(x) = sqrt(x) - 6
Yes.
It's a constant that multiplies a variable; in physics, there's a well-known one "of friction"
a coefficient
If (f - g)(x) = 2x^2 -x - 2, and f(x) = 2x^2 +1, then what is g(x)?
g(x) = -x - 3
Given the following functions, find g(2f(x)).
f(x) = x^2 - 2x + 3
g(x) = x - 4
h(x) = 2x^2 - 5x - 6
g(2f(x)) = 2x^2 - 4x + 2
Find the inverse of
f(x) = sqrt(2/3x)
f^-1(x) = 3/2x^2
Determine if the two functions are inverses of each other.
f(x) = 2sqrt(x - 5)
g(x) = 1/4x^2 - 5
No.
These coordinates named for a 17th c. man describe the position of points in space in relation to an x-axis & y-axis
Cartesian