Functions and Graphs

Functions Graphs Handbook by CK – NEW
Handbook Inequalities by Ck 
APGP Series AP GP HP Progressions Handbook by Ck

Functions and Graphs is one of the most EASIEST and SMALLEST topic of the CAT preparation. Usually coming in the exam for 2 questions.

Scope of Functions and Graphs includes:

Functions

Domain x and Range y

1. State the domain and range of the following relation. Is the relation a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

• Find the domain of f(x) = √(x + 2)

a. x = R   b. x ≥ -2  c. x < 2   d. x > 2

• Find the range of f(x) = √x- 2

a. y = R   b. y ≥ -2  c. y < 2   d. y > 2

Inverse of function f^-1

Steps:

1. Replace f(x) with y.
2. Reverse the roles of x and y
3. Solve for y in terms of x.
4. Replace y with f^-1(x).

• Find f^-1 for f(x)=3x+2

a) x-2/3 b) 3/x-2 c) x-2      d) x-4

• Find f^-1 for f(x)=x³+1

a) x-2/3 b) 3/x-2 c) x-4      d) None of these

Find function f(0), f(1), f(5), f(-3)…

• What is the value of f(x)=36^x when x=1/2?
  A. 3        B. 6        C. 18      D. 72 

• If f(x) = x³ +x²+x+2. Find the value of f(3) = ?
  A. 31      B. 41      C. 51      D. 72

Composite functions gof(x)

• If f(x) = x+1 and g(x) = x². find the fog(10)

A. x²       B. x² + 1 C. x + 1   D. (x+1)²

• Given the functions f(x) = 5x and g(x) = x²+1.. Find gof(10) = ________

1. If F(x) = 2x+3 and G(x) = (x – 3) / 2

Find gofofogogof(x).fogofog(x)

A. x²       B. x² + 1 C. x + 1   D. x

Iterative Functions

1. If f(1) = 2; f(n+1) = 2 f(n) + 5. Find f(4) = ______