A function `f: IR ->IR`, where `IR`, is the set of real numbers, is defined by `f(x) = (ax^2 + 6x - 8)/(a+6x-8x^2)` Find the interval of values of a for which is onto. Is the functions one-to-one for `a =3 ?` Justify your answer.

A function f : R rarr R, where R is the set of real numbers, is defined by : f(x)= (alpha x^2+6x-8)/(alpha+6x-8x^2) . Find the interval of values of alpha for which f is onto. Is the function one-one for alpha = 3 ? Justify your answer.

A function f:RtoR where R is the set of real numbers,is defined by f(x)=(alphax^2+6x-8)/(alpha+6x-8x^2) value of alpha for which f is onto.

A function f : R rarr R is defined as f(x) = (alpha x^2 + 6x - 8 )/(alpha + 6x - 8x^2) . Find the set of values of alpha for which is onto.

Prove that the function f : RrarrR where R is the set of all real numbers, defined as f (x) = 3x + 4 is one-one and onto . Also find the inverse function of f.

Prove that the function f : RrarrR where R is the set of all real numbers, defined as f (x) = 3x + 4 is one-one and onto . Also find the inverse function of f.

A function f:R to R is defined by f(x)=2x^(2) . Is the function f one - one and onto ? Justify your answer.

If f :IR rarrIR is defined by f(x)=x^2-3x+2 , find f(f(x))?

If R is the set of real numbers and a function f: R to R is defined as f(x)=x^(2), x in R , then prove that f is many-one into function.

Verify Lagrange's Mean Value Theorem for the function f defined by f(x) = x^3 + x^2 - 6x in the interval [-1,4]