Show that the function f: `R rarr R ` given by f(x) = `{{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):}` is not one - one

Show that the signum function f:RR, given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is neither one -one nor onto.

Show that the function f: R rarr R , f(x)= x^(4) is many-one and into.

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Show that the function f: N rarr N, given by f(1) f(2)= 1 and f(x) = x - 1 for every x gt 2, is onto but not one-one.

Show that the function f :R rarr R, given by f(x) = cos x, AA x in R is neither one-one nor onto.

Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][x^2], xne0),(0, x=0):} is onto but not one-to-one.

Show that a fuction f:RrarrR given by f(x)=ax+b, a, bin R and a!=0 is bijective.

Show that the function f(x)=1/x is decreasing in (0,oo) .

Find the value of a such that the function f defined by f(x)={{:((sinax)/(sinx), "if", x ne 0),((1)/(a), "if", x=0):} is continuous at x=0

Check the injectivity of the following function f: R rarr R is given by f(x) = x^(3)