Composition of functions - One Line Questions
1.
Which of the following is true for composition of functions? —
(f o g)(x) = f(g(x))
2.
Consider f(x) = x - 2 and g(x) = x^2. Find (g o f)(x). —
x^2 - 4x + 4
3.
Consider f(x) = |x| and g(x) = x^2. What is (g o f)(x)? —
x^2
4.
Let f(x) = x - 5 and g(x) = x + 5. What is (f o g)(x) - (g o f)(x)? —
0
5.
Let f(x) = tan(x) and g(x) = x + pi/2. Find (f o g)(0). —
-1
6.
If f(x) = 1/x and g(x) = x - 2, find (f o g)(x). —
1/(x - 2)
7.
Let f(x) = 5x - 3 and g(x) = x + 2. Find (f o g)(3). —
20
8.
If f(x) = 2x + 3 and g(x) = x - 1, find (f o g)(5). —
16
9.
Let f(x) = 2x + 1 and g(x) = x^2 - 1. Find (g o f)(2). —
24
10.
What is the value of (f o g)(1) if f(x) = x + 1 and g(x) = 2x + 1? —
4
11.
If f(x) = x^2 and g(x) = 2x. Find (f o g)(x). —
4x^2
12.
If f(x) = 2x + 3 and g(x) = x^2, find the composition (f o g)(x). —
2x^2 + 3
13.
Given f(x) = x - 1 and g(x) = 3x, find the composition (g o f)(x). —
3(x - 1)
14.
If f(x) = 3 and g(x) = x^2 + 1, what is (f o g)(x)? —
3
15.
Given f(x) = 3x + 4 and g(x) = x - 1. What is (g o f)(2)? —
5
16.
If f(x) = 2x and g(x) = 3x, what is (f o g)(x)? —
6x
17.
Let f(x) = ax and g(x) = bx. Find (f o g)(x). —
abx
18.
If f(x) = ax + b and g(x) = cx + d, find (f o g)(x). —
acx + ad + b
19.
Let f(x) = cos(x) and g(x) = x^2. Find (f o g)(sqrt(pi)). —
cos(pi)
20.
Which of the following represents the composition of function f with itself? —
f(f(x))
21.
Let f(x) = sin(x) and g(x) = x^2. Find (f o g)(pi/2). —
sin(pi^2/4)
22.
If f(x) = x^2 and g(x) = sin(x), find (g o f)(x). —
sin(x^2)
23.
If f(x) = sqrt(x^2 + 1) and g(x) = x - 1, find (f o g)(2). —
sqrt(3)
24.
Given f(x) = x^2 - 4 and g(x) = sqrt(x). Find (g o f)(3). —
sqrt(5)
25.
If f(x) = 3x - 2 and g(x) = (x+2)/3, find (f o g)(x). —
x
26.
If f(x) = x^3 and g(x) = x^(1/3), what is (f o g)(x)? —
x
27.
Let f(x) = x + 7 and g(x) = x - 7. Find (f o g)(x). —
x
28.
Let f(x) = x/2 and g(x) = 2x. Find (g o f)(x). —
x
29.
If f(x) = log(x) and g(x) = 10^x, find (f o g)(x). —
x
30.
Let f(x) = x^3 - 1 and g(x) = (x+1)^(1/3). Find (f o g)(x). —
x
31.
Consider f(x) = 1/x and g(x) = 1/x. Find (f o g)(x). —
x
32.
If f(x) = 2x + 1 and g(x) = (x-1)/2, find (f o g)(x). —
x
33.
If f(x) = x and g(x) = x^2, find (f o g)(x). —
x^2
34.
If f(x) = 2x and g(x) = x/2, what is (f o g)(x)? —
x
35.
Given f(x) = e^x and g(x) = ln(x). What is (f o g)(x)? —
x
36.
Let f(x) = 1/(x-1) and g(x) = x+1. Find the domain of (f o g)(x). —
x != 0
37.
If f(x) = 1/(x+1) and g(x) = x-1, find the domain of (f o g)(x). —
x != 0
38.
Let f(x) = 1/(x-2) and g(x) = x^2. Find the domain of (f o g)(x). —
x != sqrt(2) and x != -sqrt(2)
39.
If f(x) = x^2 + 2x + 1 and g(x) = sqrt(x), find (g o f)(x). —
sqrt(x^2 + 2x + 1)
40.
What is the domain of (g o f)(x) if f(x) = x - 1 and g(x) = sqrt(x)? —
x >= 1
41.
What is the domain of the composite function (f o g)(x) if f(x) = sqrt(x) and g(x) = x - 3? —
x >= 3
42.
If f(x) = x^2 + 1 and g(x) = sqrt(x - 1), find the domain of (f o g)(x). —
x >= 1
43.
If f(x) = x^2 and g(x) = 1/x, find (f o g)(x). —
1/x^2
44.
Given f(x) = x^2 and g(x) = x^2. Find (f o g)(x). —
x^4
45.
Let f(x) = x^2 and g(x) = x + 1. Which of the following is equal to (f o g)(x)? —
(x + 1)^2
46.
If f(x) = x^2 - 1 and g(x) = x + 1, find (g o f)(x). —
x^2 + 2
47.
If f(x) = x^2 + x and g(x) = x - 1, find (f o g)(x). —
(x - 1)^2 + (x - 1)
48.
Let f(x) = x^2 - 1 and g(x) = x^2 + 1. Find (f o g)(x). —
x^4 + 2x^2
49.
Let f(x) = x^2 and g(x) = x^3. Find (f o g)(x). —
x^6
50.
What is the range of the composite function (f o g)(x) if f(x) = x^2 and g(x) = x - 1? —
y >= 0