CAT Functions

Questions from functions have increased over the past few years. Given below is an interesting question from functions.

Question

Consider functions f(x) = x² + 2x, g(x) = √(x +1) and h(x) = g(f(x)). What are the domain and range of h(x)?

Correct Answers:
Domain = ( – infinity, +infinity)
Range – [0, infinity]

Explanatory Answer

h(x) = g(f(x)) = g(x² + 2x) = Ö( x² + 2x + 1) = Ö(x+1)² = | x + 1|

This bit is very important, and often overlooked

sqrt(9) = 3, not +3

If x² = 9, then x can be +3, but Sqrt(9) is only +3.

So, Sqrt(x²)= |x|, not +x, not + x

Domain of | x + 1| = ( -infinity, + infinity), x can take any value.

As far as the range is concerned, | x + 1| cannot be negative. So, range = [0, infinity)

December 10, 2011 CAT Functions – Questions Have given below a few questions on functions. 1. Give the domain and range of the following functions i. f(x) = x2 + 1 ii. g(x) = log (x + 1) iii. h(x) = 2x iv. f(x) = 1/ […] Posted in Functions
July 20, 2012 CAT Functions – Answers Answers to questions on Functions posted more than a while ago here 1. Give the domain and range of the following functions i. f(x) = x2 + 1 Domain = All real numbers (x can […] Posted in Functions
June 6, 2013 CAT Functions Question Qn. f(x + y) = f(x)f(y) for all x, y, f(4) = +3 what is f(-8)? A. 1/3 B. 1/9 C. 9 D. 6 Answer Choice: B Explanatory Answer f(x + 0) = f(x) […] Posted in Functions
February 27, 2014 Functions Question and Solution Question Consider set A with 'a' elements, set B with 'b' elements, set C with 'c' elements. We can define a function that is one-one but not onto from set A to set B, a function that […] Posted in Functions