Algebra

posted by .

Use composition of functions to show that the functions f(x) = 5x + 7 and
g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

  • Algebra -

    g(f(x))=1/5 (5x+7) -7/5
    = x+7/5-7/5=x

    You do the other.

  • Algebra -

    f(x)=5x+7
    g(x)=(1/5)x-7/5=(x-7)/5

    (f⁰g)(x)
    = f(g(x))
    = f((x-7)/5)
    = 5((x-7)/5)+7
    = x-7 + 7
    = x

    (g⁰f)(x)
    = g(f(x))
    = g(5x+7)
    = ((5x+7)-7)/5
    = 5x/5
    = x

    I do not know how your book displays the expression, but the first term of
    g(x)= 1/5x-7/5
    offers two possible interpretations, namely (1/5)x or 1/(5x). You might even have been able to solve the problem if it wasn't for the ambiguity.

  • Algebra -

    Thank you! I got a ton more of these to do, so you helped greatly! Thanks!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Inverse Functions

    Find the inverses of the following functions. y = 3(x - 1)^2, x >= 1 Work: x = 3(y - 1)^2 x = 3(y - 1)(y - 1) x = 3(y^2 - y - y + 1) x = 3y^2 - 6y + 3 And now what do I do!?
  2. Calculus

    Hi there, I need help with composition of functions. I need to find fog, gof, gog, and fof and their domains for the following: f(x) = square root of 2x +3 g(x) = x^2 + 1 if someone can help me asap that would be so great!
  3. CALCULUS

    show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = root(x-1) (x is greater than and equal to -1) are inverse functions. when i try f(g(x)) = x and g(f(x)) = x to show that the two functions are inverses it doesn't …
  4. calculus

    when working with composite functions, does fog=gof?
  5. Composite Functions

    f(x)=(7x+28)/(x-3) and g(x)=(3x+28)/(x-7) Find: (fog)(x) (gof)(x) (fog)(-1)
  6. algebra functions

    construct two composite functions, Evaluate each composite function for x=2. i do not fully understand functions yet can someone explain and show me what to do step by step f(x)=x+1 g(x)=x-2
  7. Algebra

    Can anyone help me with this problem? I need to show all steps and explain what is happening. A graph would be great for a visual too if possible. Thank you for any help. We define the following functions: f(x) = 2x + 5, g(x) = x^2
  8. advanced functions/precalculus

    1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)). 2. Give an example of two functions that satisfy the following …
  9. Pre=Calc

    Use composition to show that the given functions are inverses (You must show both compositions). Help?
  10. Math

    If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function?

More Similar Questions