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Hello from MrBillDoesMath!
Answer: f(g(t)) = t
Discussion:
A function and its inverse "undo" each other. Suppose that
f(t) = t^2 and g(t) = t^ (1/2)
Then
A B C
g(f(t)) = g (t^2) = (t^2) ^ (1/2) = t
A: substitute the definition of f(t), that is t^2, in the equation
B: g(t) takes the square root if its argument
C: The square root of a squared item is the item itself.
Regards, MrB
Answer:
- 19. y = x + 1
- 20. y = -2/3x - 5
- 21. y = -1/2x + 7
- 22. y = 4x - 3
Step-by-step explanation:
19. Passing through (2, 3) and PARALLEL to y = x - 4
<u>Parallel lines have equal slopes:</u>
<u>Use given point to find b:</u>
<u>The line is:</u>
20. Passing through (-6, -1) and PARALLEL 2x + 3y = 3
<u>Rewrite in the slope-intercept form:</u>
- 2x + 3y = 3
- 3y = -2x + 3
- y = -2/3x + 1
<u>The line have same slope:</u>
- y = -2/3x + b
- -1 = -2/3(-6) + b
- -1 = 4 + b
- b = - 5
<u>The line is:</u>
21. Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5
Perpendicular lines have negative-reciprocal slopes
<u>The line has the form:</u>
Find the y-intercept:
- 8 = -1/2*(-2) + b
- 8 = 1 + b
- b = 7
<u>The line is:</u>
22. Passing through (-2, -11) and PERPENDICULAR to x + 4y = 8
Perpendicular lines have negative-reciprocal slopes
<u>Rewrite in slope-intercept form:</u>
- x + 4y = 8
- 4y = -x + 8
- y = -1/4x + 2
<u>The line has the form:</u>
<u>Find y-intercept:</u>
- -11 = 4(-2) + b
- -11 = -8 + b
- b = -3
<u>The line is:</u>