Find all functions g : R → R such that for any real numbers x and y g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y).

Find all functions g : R → R such that for any real numbers x and y g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y).

Why ((x-1)^2)^(1/3)+((x+1)^2)^(1/3) is an even function?

1. Let f(x)=5x and g(x)=x^2+1, when the domain of x is all real numbers. a. Find f^-1(x). b. Find (f ° g)(7).

Given g(x)=3x^2−2x+19, find g(t-1). I am pretty sure the g (t-1) would go in the x's spot, but i am having trouble getting the amswer.

given the function P(x)=45+3x-2x2 find and simplify 3P(a+6)-17. Discuss how each value shifts/scales the function

A worker gets 18 dollars per hour for a normal work week of 40 hours and time-and-a-half for overtime. Assuming he works at least 40 hours a week, construct a function describing his weekly paycheck,...

find the inverse of the function y=8x2 which has an inverse of y-1

find the inverse of the function y=6x2 which has an inverse of y-1

g(n) = 3n + 2 f(n) = 2n2 + 5 find g(f(2))

What is the zeros of The reciprocal of arctanh (x) ? In other words. Does the reciprocal V.asymptotes become zero or not ?

Difference between function of x and function of 1/x. F(x) and F(1/x)

If the function f(t)=-5t2+20t+60 models the approximate height of an an object after it is launched then how many seconds does it take the object to hit the ground?

a.) Find the inverse of f(x) and name it g(x). Show and explain your work. b.) Use composition to show that f(x) and g(x) are inverses of each other

f(x) = x + 4 g(x) = x - 3 for which value of x is (f⁄g)(x) undefined?

A question from trigonometry and functions... If "k tanx + tan(kx) = 0", prove: ((sin kx)^2)/(sinx)^2 = (k^2)÷((1+(k^2-1)(sinx)^2))

1. The function f(x) and g(x) are defined by f(x)=2^x and g(x)= log2(1-2x) a. Write down f^-1(x). b. (i). Find and simplify (f°g)(x) (ii) Find and simplify (f°g)^-1(x) c. (i) Write...

Example:p(t_ = 2t - 1 and q(t) = -t2 - 4t - 1. Find (q - p)(t) (q - p)(t) = q(t) - p(t) q(t) - p(t) "define" (-t2 - 4t - 1) - (2t - 1) "substitute" =(-t2...

The following diagram shows the graph of y=f(x), for -4 ≤ x ≤ 5. ( Graph shows line starting at (-4, -3). It passes through the points (-2,0) and (0,1). It ends...

combination of functions

A landscape supply company charges $30 to deliver mulch. The mulch costs $23 per cubic yard. Write an equation that gives the total cost of having mulch delivered as a function of the number of cubic...