Let `f: R->R` be any function. Also `g: R->R` is defined by `g(x)=|f(x)|` for all `xdot` Then `g` is
a. Onto if `f` is onto b. One-one if `f` is one-one c. Continuous if `f` is continuous d. None of these

Let f : R to R be any function and g(x) =(1) /( f (x) ) then which of the following is / are not true ? (a) g is onto of f is onto (b) g is one - one if f is onto (c) g is continuous if is continuous (d) g is differentiable if f is differentiable

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then (a) f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

If a function f: R to R is defined as f(x)=x^(3)+1 , then prove that f is one-one onto.

Show that the function f: R->R given by f(x)=cosx for all x in R , is neither one-one nor onto.

Le f:[0,\ oo)->R\ a n d\ g: R->R be defined by f(x)=sqrt(x) and g(x)=xdot Find f+g,\ f-g,\ fg\ a n df/gdot

If f and g are one-one functions, then a. f+g is one one b. fg is one one c. fog is one one d. none of these

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto function then

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into