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2 years ago

In 45 years, Gabriela will be 4 times as old as she is now. How old is she right now

Mathematics

1 answer:

11111nata11111 [884]2 years ago

7 0

Gabriela is 15 years old right now

(15 and 3 months to be exact)

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A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

3 years ago

Does this graph represent a function? Why or why not?

Morgarella [4.7K]

Answer:

Option D is the correct answer

Step-by-step explanation:

D. Yes, because it passes the vertical line test.

7 0

2 years ago

F(x) = 2(x - 3)^2 - 2

Natali5045456 [20]

Hi. I was unsure of what exactly you wanted from this equation, so here's a quick analysis:

Domain: (-∞, ∞)

Range: (-2, ∞)

X-intercepts: (4, 0), (2, 0)

Y-intercept: (0, 16)

Axis of Symmetry: x = 3

Minimum value (vertex): (3, -2)

Standard form: y = 2x^2 - 12x + 16

4 0

3 years ago

I need help on this problem (4x+8)+(7x+3)

SpyIntel [72]

<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ You have to collect like terms

In other words, add together the values that have x in them and add together the values that don't

4x + 7x = 11x

8 + 3 = 11

The answer is 11x + 11

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

4 0

3 years ago

Read 2 more answers

(Grade6math) Can somebody plz help answer all of these in simplify form (if u know how to) thanks so much :)

Gemiola [76]

1.= 1
2.= -15
3.= -18
4.= -1
5. = -11
6. = 22

4 0

2 years ago