algebra

posted by .

Verify that the functions f and g are inverses of each other by showing f(g(x)) = x and g(f(x)) = x
f(x) = x^3 + 5
g(x) = 3sqrtx-5 ( 3 is inside check mark on the sqrt.

I am sooo totally lost on these!

  • algebra -

    g(x) takes input of "x" and gives output of "cuberoot(x - 5)" (that's what the little 3 means outside the root sign).

    Imagine feeding that into the f function.
    Note that f(anything) = (anything)^3 + 5.
    So suppose we put in what we got from doing g(x). What we got was "cubert(x - 5)". So let's put that into the f function.

    f(cubert(x-5)) = (cubert(x-5))^3+5

    But (cubert(x-5))^3 is just (x-5).

    And so (x-5)+5 is just x.

    This is how you can show that f(g(x)) = x.

    The nesting of parentheses helps you see the order in which the functions are applied. You read from the innermost out. So first function g gets applied to x and gives an expression that we can call g(x). Then the function f works on that g(x) as input and gives an output. Performing one function on the result of an earlier function is called composing functions, or composition of functions.

    So you've seen how f(g(x)) = x.

    Can you prove that g(f(x)) = x?

    Start with x and apply function f to it. Then take the result and apply function g to that, using f(x) wherever "x" appears in the rule for g(x).

  • algebra -

    Not coming out right!!!!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math help1

    Okay I am a little bit confused about one math question can you please Help me out?
  2. Algebra-Functions

    Could you please check my answers and help me with two problems?
  3. pre calculus

    verify functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) = x. f(x)= 5/(2 -x) g (x) = 2 - 5/x
  4. College Algebra

    verify that the functions of f and g are inverse of each other by showing that f(g(x))=x and g(f(x))=x; f(x)=In(x-1),g(x)=1+e^x
  5. College Algebra

    Verify the function f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x Graph the functions. f(x)=6/(1-x) g(x)=(1-6/x)
  6. Precalculus

    Verify that the functions f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. f(x)=4-x^3 g(x)=^3ã4-x
  7. precalculus

    verify the functions are inverses of each other by showing that f(g(x)) =x show work. f(x)=6/1-x g(x)= 1- 6/x
  8. College Algebra

    Verify that the function f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. Graph both the functions on the same graph. Please show all of your work. f(x)=-7/x-4 g(x)=4x-7/x
  9. pre calculus

    consider the functions f(x)=x^3-3 and g(x)=3 sqrt x+3: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverses of each other. I really need help with these, I don't get it at all.
  10. Algebra 2

    for the functions f(x) = 5x +50 and g(x) = 1/5x -10 evaluate both f(g(x)) and g(f(x)). Are these functions inverses?

More Similar Questions