<em><u>Method One</u></em>
f(g(x)) = x
<em><u>Method Two</u></em>
g(f(x)) = x
So let's pick a pair of functions and try this out.
f(x) = x^2 + 1
g(x) =sqrt(x - 1)
<em><u>Using Method 1</u></em>
f(g(x)) = (g(x)^2 + 1 You put a g(x) wherever you see an x in f(x)
f(g(x)) = [sqrt(x - 1)}^2 + 1 Substitute the right side of g(x) on the right side of f(x)
f(g(x)) = x - 1 + 1 Expand and cancel
f(g(x) = x
<em><u>Using Method 2</u></em>
g(f(x)) = sqrt(f(x) - 1) Put an f(x) wherever you see an x in g(x)
g(f(x)) = sqrt(x^2 + 1 - 1) Substitute the value of f(x) in the g(x) equation
g(f(x)) = sqrt(x^2) The 1s cancel. Take the square root of x^2
g(f(x)) = x You get x which is what you need to get.
So these two functions are the inverses of each other. Both methods confirm the results. A graph may help you to understand.
Notice how the red line (f(x) = x^2 + 1) is reflected across the green line to become the blue line (g(x) = sqrt(x - 1) ) That is another way to tell that 2 equations are inverses.
Note further that I have take the equations so that x in all three cases is ≥ 0
Answer:
-100x^2+1730x+350 - Standard from
The answer would be 10 dimes, 30 nickels and 50 pennies.
Step by Step
10 x 10=100
10 × 3=30
30×5=150
10×5=50
100+150+50=300
First you test out all the possibilities that the amount of dimes could be. When you choose a number you multiply that number by 3 since there are 3 times as many nickels as dimes, then you would multiply that number by 5. Lastly you would multiply the number of dimes by 5 because there are 5 times as many pennies as dimes. Eventually you would get the answers 10, 30, and 50.
"D.neither line symmetry nor rotational symmetry. "A line segment can have neither line symmetry nor rotational symmetry. a line segment is a line that has boundaries..
Answer:
6/14
Step-by-step explanation:
divide the numerator and denominator by 3. 18 / 3 is 6 and 42 / 3 is 14. So your answer is 6/14.