<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:
Step-by-step explanation: x+4-5=y
A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².
<h3>What is the area of the triangle?</h3>
The Area of one triangular face can be calculated as;
A = area of triangle = ½ x b x h
Where,
b = 32 ft
h = 20 ft
A = ½ x 32 x 20 = 16 x 20
A = 320 ft²
Area of 1 triangular face = 320 ft²
B.
Total surface area = area of the 4 triangular faces + area of the base of the square pyramid
T.S.A = 4(320) + (s²)
Where,
s = 32 ft
T.S.A = 4(320) + (32²)
T.S.A = 1,280 + 1,024
= 2,304 ft²
A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².
Learn more about pyramids here:
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