Question

Use the cancellation equations to show that the following functions f and g are inverses of one another f(x)= x-5/2x+3 g(x)= 3x+5/1-2x please explain

Answer #1

**Solution:**

and are inverses of each other.

1. Show that U=f(x) + e^(-3x) g(2x+y), where f and g are
arbitrary smooth functions, is a general solution of Uxy- 2Uyy
+3Uy=0. Do not solve!

Suppose the following functions have inverses on their
domains.
(1) f(x) = 4ecos(4x). Find and explicit
formula for f-1(y).
(2) g(x) = log3(tan(x)). Find an explicit
formula for g-1(y).

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

In the study of logarithns and exponentials we first learn about
one-to-one functions and inverse functions because the logarithm
and exonential functions are inverse functions. Many conceptsare
involved in the study of these two topics. Please demonstrate your
understanding of the concepts by following the discussion guideline
below: Start with a medium difficulty level function and then find
its inverse function (should take at least 3 steps) and write the
inverse function in terms of x. Name the original function...

In the study of logarithns and exponentials we first learn about
one-to-one functions and inverse functions because the logarithm
and exonential functions are inverse functions. Many conceptsare
involved in the study of these two topics. Please demonstrate your
understanding of the concepts by following the discussion guideline
below:
Start with a medium difficulty level function and then find its
inverse function (should take at least 3 steps) and write the
inverse function in terms of x. Name the original
function f(x)...

Please find the derivative of the following functions and show
full work:
1) f (x) = sin^3 (cos(2x))
2) y = e^cosh5x
***the cosh5x in #2 is all to the power of e.

Number Theory: Please show all work.
Solve each of the following equations for the unknown variable X
≡ 0, 1, 2, 3, 4, 5, 6 mod 7.
(i) 2X + 5 ≡ 6 mod 7.
(ii) 3X + 5 ≡ 6 mod 7.

1- For the following functions, find all critical numbers
exactly.
f(x) = x − 2 sin x for −2π < x < 2π
f(x) = e^−x −e^−3x for x > 0
f(x) = x^5 − 2x^3

Determine which of the following functions are one to one
and explain your reasoning.
1. f(x)=
x2-3x-10
2. g(x)=
-2x3+1

Find the derivative of the following functions
(a) f(x) = ln(√x3 −2x)
(b) g(x) =√x2 + 3 x3 −5x + 1
.

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