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

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

Let the function f: RvecR be defined by f(x)=x+sinxforx in Rdot Then f is one-to-one and onto one-to-one but not onto onto but not-one-to-one neither one-to-one nor onto

If f : R to R is defined by f (x) = |x| -5, then the range of f is ……………

If f: R to R and g: R to R are defined by f(x)=x^(5) and g(x)=x^(4) then check if f, g are one-one and fog is one-one?

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into

Let f: A to B and g: B to C be two functions. Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

Let f:R->R be a continuous function such that |f(x)-f(y)|>=|x-y| for all x,y in R ,then f(x) will be