#1
What is the result of composing the functions f(x) = 2x + 3 and g(x) = x^2?
2x^2 + 9
ExplanationComposition of two functions.
#2
If f(x) = x^2 - 5x + 6 and g(x) = 3x - 2, what is f(g(2))?
14
ExplanationSubstitute g(2) into f(x).
#3
If f(x) = 2x - 1 and g(x) = 3x + 2, what is (f o g)(x)?
6x + 5
ExplanationComposition of two linear functions.
#4
Given f(x) = x^2 and g(x) = √x, what is (g o f)(x)?
√x
ExplanationSquare root function composition.
#5
If f(x) = x^3 and g(x) = √x, what is (f o g)(x)?
x^(3/2)
ExplanationCube function composed with square root.
#6
Given f(x) = 3x - 1 and g(x) = 2x + 5, what is (g o f)(x)?
6x - 7
ExplanationComposition of two linear functions.
#7
If f(x) = x^2 - 4x + 4 and g(x) = √x + 1, what is f(g(x))?
x^2 + 1
ExplanationSubstitute g(x) into f(x).
#8
If f(x) = 3x + 1 and g(x) = x^2 - 2x, what is (f o g)(x)?
9x^2 - 6x + 1
ExplanationComposition of linear and quadratic functions.
#9
If f(x) = 2x + 3 and g(x) = 4x - 1, what is (f o g)(x)?
8x + 1
ExplanationComposition of two linear functions.
#10
Given f(x) = x^2 and g(x) = 1/x, what is (f o g)(x)?
x^2
ExplanationComposition of quadratic function with reciprocal function.
#11
If f(x) = 2x^2 - 3x + 1 and g(x) = x^2 + 5, what is (g o f)(x)?
4x^4 + 12x^3 - 4x^2 + 24x + 6
ExplanationComposition of two quadratic functions.
#12
If f(x) = x^3 + 2x^2 - x + 1 and g(x) = √x + 1, what is f(g(x))?
x^(3/2) + 2√x + 1
ExplanationSubstitute g(x) into f(x).
#13
Given f(x) = x^2 and g(x) = 2x + 1, what is (g o f)(x)?
4x^2 + 1
ExplanationComposition of quadratic function with linear function.
#14
If f(x) = x^2 + 2x and g(x) = √x, what is (g o f)(x)?
√(x^2 + 2x)
ExplanationComposition of quadratic function with square root.