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Snowcat [4.5K]
1 year ago
14

Verify if f(x)= 5-3x/2 and g(x)= 5-2x/3 are inverses. Please show step by step.

Mathematics
1 answer:
mestny [16]1 year ago
7 0

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

<h3>Inverse of functions</h3>

In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))

Given the function

f(x)= 5-3x/2 and

g(x)= 5-2x/3

f(g(x)) = f(5-2x/3)

Substitute

f(g(x)) = 5-3(5-2x)/3)/2

f(g(x)) = (5-5+2x)/2

f(g(x)) = 2x/2

f(g(x)) = x

Similarly

g(f(x)) = 5-2(5-3x/2)/3

g(f(x)) = 5-5+3x/3

g(f(x)) = 3x/3

g(f(x)) =x

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

Learn more on inverse of a function here: brainly.com/question/19859934

#SPJ1

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maxonik [38]

Answer:

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Step-by-step explanation:

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8 0
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algol13
Answers:
x = 24
y = 8√3
Explanation:

1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.

2) The variables given represent:

x: adjacent-leg to angle 30°
y: opposite length to angle 30°

3) sine ratio:

sin 30° = opposite-leg / hypotenuse = y / (16√3)

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4) cosine ratio

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4 0
3 years ago
Help me asap!!!! please
Lubov Fominskaja [6]

Answer:

x = 3 should be the answer

Step-by-step explanation:

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6 0
2 years ago
The line of symmetry is involved in which transformation?
BARSIC [14]

Answer:

Reflection

Step-by-step explanation:

The line of symmetry is involved in reflection transformations- when you reflect a graph, you can see the line that separates the original image from its reflected one.

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8 0
3 years ago
The graph of a line has a slope of -7 and a y intercept of (0,0). Rewrite the equation in standard form (Ax+By=C) with a positiv
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Answer:

the equation of the line is 7x + y = 0 .

Step-by-step explanation:

in the standard form of the line that is Ax +By = C we can write it in the form of

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y = \frac{-A}{B}x +\frac{C}{B}

which is in the form of y = mx +c

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comparing  y = \frac{-A}{B}x +\frac{C}{B} and  y = mx +c

we get that \frac{-A}{B} =m and \frac{-C}{B} = c

since it is given that slope of the line is -7 therefore m = -7 and c = 0

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therefore C = 0 , A = 7 and B = 1

therefore the equation becomes 7x + y = 0

3 0
3 years ago
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