1. find the solution
sqrt 2x - 8 + 2 = 4
2. let f(x) = 3x+6 and g(x) and = -x-4. find f(x) - g(x)
3. find the inverse of the function.
y = 2x + 5
4. rewrite the expression to make it easier to graph. what are the transformations to the parent function?
^3 sqrt 8x - 24 + 4
5. suppose f(x) = 3x-1 and g(x) = 4x+3. find f(g(2)).
1. To find the solution, we can start by isolating the square root term:
sqrt(2x - 8) + 2 = 4
Subtract 2 from both sides:
sqrt(2x - 8) = 2
Square both sides:
2x - 8 = 4
Add 8 to both sides:
2x = 12
Divide both sides by 2:
x = 6
Therefore, the solution is x = 6.
2. To find f(x) - g(x), we need to subtract the values of g(x) from f(x):
f(x) = 3x + 6
g(x) = -x - 4
f(x) - g(x) = (3x + 6) - (-x - 4)
= 3x + 6 + x + 4
= 4x + 10
Therefore, f(x) - g(x) = 4x + 10.
3. To find the inverse of the function y = 2x + 5, start by swapping the x and y variables:
x = 2y + 5
Next, solve for y:
x - 5 = 2y
(x - 5)/2 = y
Therefore, the inverse of the function is y = (x - 5)/2.
4. To make the expression easier to graph, we can simplify it by removing the square root:
^3 sqrt(8x - 24) + 4
Since the square root is cubed, it can be written as:
(8x - 24)^(1/3) + 4
This simplification makes it easier to graph the function. The transformations to the parent function are:
- The graph is shifted 24 units to the right (x + 24)
- The graph is compressed horizontally by a factor of 8 (x/8)
- The graph is shifted 4 units upwards (+4)
5. To find f(g(2)), we first need to find g(2):
g(x) = 4x + 3
g(2) = 4(2) + 3
= 8 + 3
= 11
Next, substitute g(2) back into f(x):
f(x) = 3x - 1
f(g(2)) = 3(11) - 1
= 33 - 1
= 32
Therefore, f(g(2)) = 32.