Function and their graphs

[asimon2005]

My teacher wasn't at school to teach us how to do this, but she told us to get ready because next week we have test on this stuff.

These equations deal with finding F(gx) or G(fx).

45. f(x)= ?(x+6), g(x)= x^2-5

47. f(x)=|x+3|, g(x)= 2x-1

THese next set of problems deal with the inverse function.

1. f(x)=6x

3. f(x)=x+7

7. f(x)=3?(X)

In ex. 9-20 show that f and g are inverse function algebraically.

9. f(x)=-7/2x-3, g(x)= -2x=6/7

13. f(x)= -?(x-8); g(X)= 8 +x^2, x < or equal to 0

15. f(x)=x^3, g(x)=3?(x)

19. f(x)=1-x^3, g(x)=3?(1-x)

In Ex. 53-62, find the inverse function of f. Describe relationship between the graphs.

53. f(x)=2x-3

59. f(x)=?(4-x^2), 0 < equal to x < equal to 2.

61. f(x)= 4/x

 

[fasteddie65]

My teacher wasn't at school to teach us how to do this, but she told us to get ready because next week we have test on this stuff.

These equations deal with finding F(gx) or G(fx).

45. f(x)= ?(x+6), g(x)= x^2-5

47. f(x)=|x+3|, g(x)= 2x-1

THese next set of problems deal with the inverse function.

1. f(x)=6x

3. f(x)=x+7

7. f(x)=3?(X)

In ex. 9-20 show that f and g are inverse function algebraically.

9. f(x)=-7/2x-3, g(x)= -2x=6/7

13. f(x)= -?(x-8); g(X)= 8 +x^2, x < or equal to 0

15. f(x)=x^3, g(x)=3?(x)

19. f(x)=1-x^3, g(x)=3?(1-x)

In Ex. 53-62, find the inverse function of f. Describe relationship between the graphs.

53. f(x)=2x-3

59. f(x)=?(4-x^2), 0 < equal to x < equal to 2.

61. f(x)= 4/x

****************************

47. f(x) = |x + 3|, g(x) = 2x - 1

To find f(g(x)), replace the x in f(x) by g(x). In other words, f(g(x)) = |g(x) + 3| = |(2x - 1) + 3| = |2x + 2|

3. f(x) = x + 7

To find the inverse of f(x), interchange the x and y variables and solve for y.

y = x + 7
x = y + 7
x - 7 = y

The inverse function is g(x) = x - 7.

19. f(x) = 1 - x^3, g(x) = 3?(1 - x)

f(g(x)) = 1 - (g(x))^3 = 1 - 3?(1 - x)^3 = 1 - (1 - x) = 1

g(f(x)) = 3?(1 - f(x)) = 3?(1 - (1 - x^3)) = 3?x^3 = x

As far as the relationship between the graphs of a function and its inverse, the graphs are symmetric to the graph of y = x.

 

[stapel]

My teacher wasn't at school to teach us how to do this, but she told us to get ready because next week we have test on this stuff.

So you're needing lessons. Since we cannot here reasonably replace the missing hours of instruction, you will need to study from your book, and then use other resources to fill in any gaps. The following lists of lessons may be helpful.

. . . . .Google results for "function composition"
. . . . .Google results for "inverse functions"

Once you have studied at least two lessons from both links, please attempt the exercises. If you get stuck, you will then be able to reply with a clear listing of your work and reasoning so far, so the helpers can "see" where you are having trouble and can help you get "un-stuck".

Thank you!