Even / Odd Functions — CAT Previous-Year Questions
10 previous-year questions on Even / Odd Functions from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Even / Odd Functions · CAT PYQs
If f(5 + x) = f(5 - x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is
Given below are three graphs made up of straight-line segments shown as thick lines. In each case choose the answer as
1. if f(x) = 3 f(–x);
2. if f(x) = –f(–x);
3. if f(x) = f(–x); and
4. if 3 f(x) = 6 f(–x), for x ≥ 0.
Given below are three graphs made up of straight-line segments shown as thick lines. In each case choose the answer as
1. if f(x) = 3 f(–x);
2. if f(x) = –f(–x);
3. if f(x) = f(–x); and
4. if 3 f(x) = 6 f(–x), for x ≥ 0.
Given below are three graphs made up of straight-line segments shown as thick lines. In each case choose the answer as
1. if f(x) = 3 f(–x);
2. if f(x) = –f(–x);
3. if f(x) = f(–x); and
4. if 3 f(x) = 6 f(–x), for x ≥ 0.
Answer the next 4 questions based on the following information.
In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straightline segments, shown as solid lines, in the domain x ∈ (−2, 2).
Choose the answer as
a. if F1(x) = –F(x)
b. if F1(x) = F(–x)
c. if F1(x) = –F(–x)
d. if none of the above is true
Answer the next 4 questions based on the following information.
In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straightline segments, shown as solid lines, in the domain x ∈ (−2, 2).
Choose the answer as
a. if F1(x) = –F(x)
b. if F1(x) = F(–x)
c. if F1(x) = –F(–x)
d. if none of the above is true
Answer the next 4 questions based on the following information.
In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straightline segments, shown as solid lines, in the domain x ∈ (−2, 2).
Choose the answer as
a. if F1(x) = –F(x)
b. if F1(x) = F(–x)
c. if F1(x) = –F(–x)
d. if none of the above is true
Answer the next 4 questions based on the following information.
In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straightline segments, shown as solid lines, in the domain x ∈ (−2, 2).
Choose the answer as
a. if F1(x) = –F(x)
b. if F1(x) = F(–x)
c. if F1(x) = –F(–x)
d. if none of the above is true
Answer the next 2 questions based on the information given below:
A function f(x) is said to be even if f(–x) = f(x), and odd if f(–x) = –f(x). Thus, for example, the function given by f(x) = x2 is even, while the function given by f(x) = x3 is odd. Using this definition, answer the following questions.
The function given by f(x) = |x|3 is
Answer the next 2 questions based on the information given below:
A function f(x) is said to be even if f(–x) = f(x), and odd if f(–x) = –f(x). Thus, for example, the function given by f(x) = x2 is even, while the function given by f(x) = x3 is odd. Using this definition, answer the following questions.
The sum of two odd functions