1.) f(x) = 3x - 7 and g(x) = -2x - 6. Find (f ° g)(4)
2.) What is the inverse of the given relation?
y = 3x + 12
3.) Rewrite ^3 sqrt 27x - 81 - 5 to make it easy to graph using translation. Describe the graph.
I need help with my last 3 questions.
I only need help with #1 I figured out 2 and 3
(fºg)(4) means f[g(4)]
g(4) = -2(4) - 6 = ?
f(?) = 3? - 7
(f°g)(x) = f(g) = 3g-7 = 3(-2x-6)-7 = -6x-25
Now plug in x=4 and compare with the answer you got from Scott
1.) To find (f ° g)(4), first evaluate g(x) at x = 4, and then substitute that value into f(x).
Start by determining the value of g(4) by substituting x = 4 into the function g(x):
g(4) = -2(4) - 6 = -8 - 6 = -14
Now, substitute g(4) = -14 into the function f(x):
f(g(4)) = f(-14)
Using the function f(x) = 3x - 7, substitute -14 for x:
f(-14) = 3(-14) - 7 = -42 - 7 = -49
Therefore, (f ° g)(4) = -49.
2.) To find the inverse of the given relation y = 3x + 12, interchange x and y, and then solve for y.
Start by interchanging x and y, yielding: x = 3y + 12
Now solve for y. Subtract 12 from both sides of the equation:
x - 12 = 3y
Divide both sides by 3 to isolate y:
y = (x - 12)/3
Thus, the inverse of the given relation is y = (x - 12)/3.
3.) The expression "^3 sqrt 27x - 81 - 5" can be rewritten as follows to make it easier to graph using translation:
^3 sqrt 27x - 86
To simplify this expression, start with the innermost operation, which is taking the cubic root of the quantity (27x - 86).
The graph of y = ^3 sqrt 27x - 86 would be a cubic root function that is translated 86 units downward from the original cubic root function. The graph would retain the shape of a cubic root function, but would be shifted downward along the y-axis.
As for the description of the graph, it would be wider than the original cubic root function and would pass through the point (0, -86). The graph would extend both to the left and to the right of the y-axis.