Question

In: Math

The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and...

The function f(x)=3x+2 is one-to-one

a) find the inverse of f

b) State the domain and range of f

c) State the domain and range of f^-1

d) Graph f,f^-1, and y=x on the same set of axes

Expert Solution

Solution : ( a )

-------------------------------------------------------------------------------------------------------------------

Solution : ( b )

-------------------------------------------------------------------------------------------------------------------------------

Solution : ( c )

milcah answered 2 years ago

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...

Consider the function. f(x) = x^2 − 1, x ≥ 1 (a) Find the inverse function...

Consider the function. f(x) = x^2 − 1, x ≥ 1 (a) Find the inverse function of f. f ^−1(x) = (b) Graph f and f ^−1 on the same set of coordinate axes. (c) Describe the relationship between the graphs. The graphs of f and f^−1 are reflections of each other across the line ____answer here___________. (d) State the domain and range of f and f^−1. (Enter your answers using interval notation.) Domain of f Range of f Domain...

Let f(x) = x / (4−x^2) . (a) Find the domain and intercepts of f(x). (b)...

Let f(x) = x / (4−x^2) . (a) Find the domain and intercepts of f(x). (b) Find all asymptotes and limits describing the end behavior of f(x). (c) Find all local extrema and the intervals on which f(x) is increasing or decreasing. (d) Find the inflection points and the concavity of f(x). (e) Use this information to sketch the graph of f(x)

Find the domain for each function please explain. f(x)=10x^2 + x f(x)= -2/x^2

Find the domain of the function g(x) = square root of 3x+3

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6...

How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6 f(g)= (x+2) / x^2-1 f(g)= x^4 / x^2+x-6 f(g)= sqrt (x+1) f(g)= sqrt (x^2+9)

Find the inverse of the function g : R ! R, g(x) = { 3x +...

Find the inverse of the function g : R ! R, g(x) = { 3x + 5 if x is less than equal to 6 5x - 7 if x > 6