The inverse of f(x) = `{(x,if,xlt1),(x^(2),if,1lt=xlt=4"is"),(8sqrt(x),if,xgt4):}`

If the function f is defined as f(x) = {(3x-2,xgt3),(x^(3)-2,-2lt=xlt=2),(2x+1,xlt-2):} Then find the values, if exists f (4), f (-4), f(0), f(-7).

Write the values of f at -4,1,-2,7,0 if f(x)= {(-x+4,if,-ooltxlt=-3),(x+4,if,-3ltxlt-2),(x^(2)-x, if," "-2lt=xlt1),(x-x^(2), if, " "1lt=xlt7),(0,"", " ""otherwise"):}

If X is the random variable with distribution function F(x) given by , F(x) = {{:(0,xlt0),(x^2,0lt=xlt1),(1,xgt1):} then find (i) the Probability density function f(x)

If the function f: R to R is defined by f (x) {:{( 2x+1 ,xlt-1) ,( x^(2) -1,le x lt 3 ),( 3x-2, xge 3) :} "Find " (f(-1) +f(3))/( 2)

The probability density function of X is f(x) = {(x,0 ltxlt1),(2-x, 1lt=xlt2),(0,"otherwise"):} Find (i) P(0.2 lt=X lt0.6) (ii) P(1.2lt= X lt 1.8) (iii) P(0.5 lt=X lt 1.5)

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

If X is the random variable with distribution function F(x) given by , F(x) = {(o,xlt0),(x,0lt=xlt1),(1,1lt=x):} then find (i) the probability density function f(x) (ii) P(0.2lt=Xlt=0.7) .

Find the probability mass function f(x) of the discrete random variable X whose cumulative distribution function F(x) is given by F (x) = {(0,-ooltxlt-2),(0.25,-2lt=xlt-1),(0.60,-1lt=xlt0),(0.90,0lt=xlt1),(1,1lt=xltoo):} Also find (i) P (X lt0 ) and (ii) P (Xgt=-1) .