IIT-JEE 1982Question 1
If $p,q,r$ are any real numbers, then
Functions
Solution
If $p\ge q$ then $\frac12(p+q-|p-q|)=\frac12(p+q-p+q)=q=\min(p,q)$, similarly for $p<q$. A fails for $r\le\max(p,q)$ (equality), C fails always since $\min\le\max$.Functions - JEE Mathematics question (IIT-JEE 1982)
More from Functions
- Let f:mathbb R- \-frac12 \tomathbb R and g:mathbb R- \-frac52 \tomathbb R be defined as f(x)=(2x+3)/(2x+1)…
- If the domain of the function f(x)=fraccos^-1sqrtx^2-x+1sqrtsin^-1 ((2x-1)/(2) ) is the interval…
- Let f:(0,1)tomathbbR be defined by f(x)=(b-x)/(1-bx), where b is a constant such that 0<b<1 . Then
- If the function f:R-\1,-1\to A defined by f(x)=fracx^21-x^2 , is surjective, then A is equal to
- Let S=(0,1)cup(1,2)cup(3,4) and T=\0,1,2,3\ . Then which of the following statements is(are) true?
- The graph of the function y=f(x) is symmetrical about the line x=2 , then
- If f(x)=|x-2| and g(x)=f[f(x)] , then g'(x)= ______ for x>20 .
- The domain of the function f(x)=sin^-1 (frac3x^2+x-1(x-1)^2 )+cos^-1 ((x-1)/(x+1) ) is :