Q Let the Function

Let A = R - (-5) and B = R . Let the function f: A to B be defined as f(x) = (5x + 4)/( x + 5) , x in A . Show that f is an injective function.

Let f:N rarr R be the function defined by f(x)=(2x-1)/2 and g:Q rarr Q be another function defined by g(x)=x+2 then (gof)(3/2) is

Let f : N rarr R be the function defined by f(x) = (2x-1)/(2) and g : Q rarr R be another function defined by g(x) = x + 2. Then (gof) ((3)/(2)) is

Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q is a bijection.

Let p and q be real numbers such that the function f(x)={{:(p^(2)+qx","xge1),(-5px^(2)-6","xlt1):} is derivable for all x in R . Then sum of all possible values of p is

Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Also, find f^(-1) .

Let the function q be defined by q(x)=a(x-h)^(2) , where h is a positive constant, and a is a negative constant. For what value of x will the function q have its maximum value?

The function p is defined as p(x)= x^2-3x . If the function q is defined as q(x)=p(x)-4, what is the value of q(10)?

Let f(x) =x and g(x)=|x| be two real-valued functions, check whether the functions are one -one.

Neither q nor w is a state function but q +w is a state function. Explain why?