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aniked [119]
2 years ago
9

Verify that f and g are inverses functions using composition , show your steps

Mathematics
1 answer:
pshichka [43]2 years ago
5 0

Answer:

See explanations below

Step-by-step explanation:

Given the functions

f(x) = 12x - 12

g(x) = x/12 - 1

To show they are inverses, we, must show that f(g(x)) = g(f(x))

f(g(x)) = f(x/12 - 1)

Replace x with x/12 - 1 into f(x)

f(g(x)) =12((x-12)/12) - 11

f(g(x)) =  x-1 - 1

f(g(x)) =x - 2

Similarly for g(f(x))

g(f(x)) = g(12x-12)

g(f(x)) =(12x-12)/12 - 1

12(x-1)/12 - 1

x-1 - 1

x - 2

Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other

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Diagram shows two perpendicular straight lines,OB and CBD,drawn on a Cartesian plane.
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Answer: (a) y = -3x + 10

               \bold{(b)\x=\bigg(\dfrac{10}{3},0\bigg)}  

<u>Step-by-step explanation:</u>

The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.

Step 1: Find the slope of OB using the formula: m=\dfrac{y_2-y_1}{x_2-x_1}

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)

m=\dfrac{1-0}{3-0} = \dfrac{1}{3}

Step 2: Find the slope of CD (opposite and reciprocal of OB)

m = \dfrac{1}{3}\qquad m_\perp=-\bigg(\dfrac{3}{1}\bigg) = -3

Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)

(x₁, y₁) = (3, 1) because it is the point the line will pass through

y - 1 = -3(x - 3)

y - 1 = -3x + 9      <em>distributed -3 into (x - 3)</em>

y      = -3x + 10    <em>added 1 to both sides</em>

***********************************************************************

The x-intercept of DQ is the same x-intercept as CD.  The x-intercept is when y = 0

y = -3x + 10

0 = -3x + 10

-10 = -3x       subtracted 10 from both sides

\dfrac{10}{3}=x    <em>divided both sides by -3</em>


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